wikiHow's Content Management Team carefully monitors the work from our editorial staff to ensure that each article is backed by trusted research and meets our high quality standards. Easy to follow. If it is zero, you can find the inverse of the matrix. ... Inverse of a 3x3 matrix Cofactor matrix. You can follow these steps to find the inverse of a matrix that contains not only numbers but also variables, unknowns or even algebraic expressions. 3x3 identity matrices involves 3 rows and 3 columns. Apart from the Gaussian elimination, there is an alternative method to calculate the inverse matrix. Definition. Notice the colored elements in the diagram above and see where the numbers have changed position. ", "The photos were so understandable and clearly shown. Then I inverse it using the algorithm to inverse a 3x3 matrix of real numbers but look like it's not correct. The matrix function will not read the number properly. Example: find the Inverse of A: It needs 4 steps. Thanks. Set the matrix (must be square) and append the identity matrix of the same dimension to it. Can I solve equations with fractions by using Cramer's rule? Mathematically, this definition is pretty simple. Let A be square matrix of order n. Then, A−1 exists if and only if A is non-singular. Reduce the left matrix to row echelon form using elementary row operations for the whole matrix (including the right one). Elements of the matrix are the numbers which make up the matrix. Divide each term of the adjugate matrix by the determinant to get the inverse. And the next thing that we can do is find the determinant of it, which we already have a good bit of practice doing. To find the Inverse of a 3 by 3 Matrix is a little critical job but can be evaluated by following few steps. Let A be a square matrix of order n. The adjoint of square matrix A is defined as the transpose of the matrix of minors of A. Continue on with the rest of the matrix in this fashion. A ij = (-1) ij det(M ij), where M ij is the (i,j) th minor matrix obtained from A after removing the ith row and jth column. Note : Let A be square matrix of order n. Then, A −1 exists if and only if A is non-singular. Calculating the inverse of a 3x3 matrix by hand is a tedious job, but worth reviewing. In general, you can skip the multiplication sign, so `5x` is equivalent to `5*x`. ", "I didn't know how to find the inverse. wikiHow's. ", "The steps are easy to follow, especially with the example given. "Inverse of matrix 3x3|(1&1&0@1&1&1@0&2&1)|". AB = BA = I n. then the matrix B is called an inverse of A. In order to find inverse of a matrix, first we have to find |A|. To find the inverse of a 3x3 matrix, we first have to know what an inverse is. Last Updated: November 5, 2020 ", "Great pictures, split into steps. ", "It really helps me for my final exam tomorrow. May God bless you for this article. This article is so much clearer than other articles. Let A be a square matrix of order n. If there exists a square matrix B of order n such that. If not, go on to the next steps • Then, transpose the first matrix • Next, find the determinant of the 2x2 matrixes How do I find specific numbers in a 3x3 matrix? For example, using the TI-86, enter the Math function, then select Misc, and then Frac, and Enter. Formula to find inverse of a matrix It is much less intuitive, and may be much longer than the previous one, but we can always use it … Treat the remaining elements as a 2x2 matrix. The inverse of a matrix A is another matrix denoted by A−1and isdefined as: Where I is the identitymatrix. The first step is to create a "Matrix of Minors". The use of different color was a good way to see the idea clearly. We know ads can be annoying, but they’re what allow us to make all of wikiHow available for free. For a review of the identity matrix and its properties, see, Remember that row reductions are performed as a combination of scalar multiplication and row addition or subtraction, in order to isolate individual terms of the matrix. Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here. How do I program a matrix inverse in MATLAB? Doing my matrices homework and there's a question about finding the inverse of the following matrix: 0 2 3 2 0 0 1 -1 0 I know how to find the inverse of these, but its just that this one has a 0 as the first number so I don't know how to get the 2nd and 3rd numbers in the 1st column to equal 0 because of this? Inverse of a matrix in MATLAB is calculated using the inv function. determinant(A) is not equal to zero) square matrix A, then an n × n matrix A-1 will exist, called the inverse of A such that: AA-1 = A-1 A = I, where I is the identity matrix. As a result you will get the inverse calculated on the right. In the example shown above, if you want the minor matrix of the term in the second row, first column, you highlight the five terms that are in the second row and the first column. AB = BA = I n. then the matrix B is called an inverse of A. Check that your result is accurate, whichever method you choose, by. Answer There are mainly two ways to obtain the inverse matrix. The (i,j) cofactor of A is defined to be. Mathematically, these are equivalent. ", "It helped me in the concept of Hill Cipher Algorithm. We're nearing the home stretch of our quest to find the inverse of this three-by-three matrix here. If the determinant of the matrix is equal to 0, then it does not have an inverse. Finding Adjoint of a Matrix Examples. Just check out the equation below: This method is only good for finding the inverse of a 2 × 2 matrix.We'll see how this method works via an example. We're going to use the identity matrix I in the process for inverting a matrix. If it is zero, then the answer has been found. If necessary, you can use your calculator’s arrow keys to jump around the matrix. Division by zero is not defined. For example, the inverse of 8is 18, the inverse of 20 is 120 and so on.Therefore, a number multiplied by its inverse will always equal 1. A singular matrix is the one in which the determinant is not equal to zero. Adulting 101: The credit building course from wikiHow. If a determinant of the main matrix is zero, inverse doesn't exist. The associated inverse matrix will have only integer elements as well. Similarly, since there is no division operator for matrices, you need to multiply by the inverse matrix. This step has the most calculations. This is sometimes referred to as the adjoint matrix. Learn to find the inverse of matrix, easily, by finding transpose, adjugate and determinant, step by step. Let A be a square matrix of order n. If there exists a square matrix B of order n such that. Given the matrix $$A$$, its inverse $$A^{-1}$$ is the one that satisfies the following: Learn more... Inverse operations are commonly used in algebra to simplify what otherwise might be difficult. Check the determinant of the matrix. This article was co-authored by our trained team of editors and researchers who validated it for accuracy and comprehensiveness. Let A be a square matrix of order n. If there exists a square matrix B of order n such that. If you wish to enter a negative number, use your calculator’s negative button (-) and not the minus key. If you want to learn how to find the inverse using the functions on a scientific calculator, keep reading the article! Find the inverse (if it exists) of the following: Since |A|  =  2 ≠ 0, it is non singular matrix. If you receive an error message when you enter the inverse key, chances are that your original matrix does not have an inverse. Since |A|  =  2 ≠ 0, it is non singular matrix. ), This article was co-authored by our trained team of editors and researchers who validated it for accuracy and comprehensiveness. Find the determinant of each minor matrix by cross-multiplying the diagonals and subtracting, as shown. wikiHow marks an article as reader-approved once it receives enough positive feedback. Show Instructions. Computer programs exist that work out the inverses of matrices for you, All tip submissions are carefully reviewed before being published, Not all 3x3 matrices have inverses. "Studying for a CSET in math and have to review matrices. A matrix is a generalization of a vector. Sal shows how to find the inverse of a 3x3 matrix using its determinant. It is denoted by adj A. You made my life easy. Yes, you can multiply a row in a matrix by -1 as long as you multiply all numbers in a row. Find the inverse matrix of the 3×3 matrix A=[72−2−6−1262−1]using the Cayley-Hamilton theorem. The second element is reversed. find the inverse of matrix using calculator , If you want to calculate inverse of matrix then by using calculator you can easily calculate. $\begingroup$ That's not correct; multiplying the original matrix with the supposed inverse doesn't yield the identity matrix; look at the dot product of the original third row with the inverse's third column. Thanks. FINDING ADJOINT OF A MATRIX EXAMPLES. Create … For each element of the matrix: ignore the values on the current row and column The determinant of matrix M can be represented symbolically as det(M). A square matrix is singular only when its determinant is exactly zero. Use the ad - bc formula. Include your email address to get a message when this question is answered. Therefore, dividing every term of the adjugate matrix results in the adjugate matrix itself. A-1 exists. To find the inverse of a matrix A, i.e A-1 we shall first define the adjoint of a matrix. Find the adj of the co-factor matrix, then divide through each term by the determinant. How can I create a 3x3 matrix without any fractions in its original form and inverse form? Thus, similar toa number and its inverse always equaling 1, a matrix multiplied by itsinverse equals the identity. In this tutorial, we are going to learn about the matrix inversion. Otherwise, it doesn't. A matrix for which you want to compute the inverse needs to be a square matrix. We use cookies to make wikiHow great. How do you find the inverse? How do I evaluate the inverse of the matrix {1 2 -4}{0 -2 3}{5 0 4}? Note that the (+) or (-) signs in the checkerboard diagram do not suggest that the final term should be positive or negative. Is it necessary to A = IA for elementary row operation, or can it be written as A = AI? By using our site, you agree to our. For more on minor matrices and their uses, see. Example. A matrix that has no inverse is singular. Next, transpose the matrix by rewriting the first row as the first column, the middle row as the middle column, and the third row as the third column. Step 1: Matrix of Minors. A matrix X is invertible if there exists a matrix Y of the same size such that X Y = Y X = I n, where I n is the n-by-n identity matrix. A = AI is written for elementary column operation, but elementary row operation is always written A = IA. |A|  =  cos α [cos α - 0] - 0[0 - 0] + sin α[0 + sin α]. One is to use Gauss-Jordan elimination and the other is to use the adjugate matrix. From there, apply the +- matrix and then divide by the determinant. You need to calculate the determinant of the matrix as an initial step. You may want to go back and calculate the determinant to find out. The third element keeps its original sign. ", "Just checking if I understood the method well, and which way may be faster. Solving linear equations using elimination method, Solving linear equations using substitution method, Solving linear equations using cross multiplication method, Solving quadratic equations by quadratic formula, Solving quadratic equations by completing square, Nature of the roots of a quadratic equations, Sum and product of the roots of a quadratic equations, Complementary and supplementary worksheet, Complementary and supplementary word problems worksheet, Sum of the angles in a triangle is 180 degree worksheet, Special line segments in triangles worksheet, Proving trigonometric identities worksheet, Quadratic equations word problems worksheet, Distributive property of multiplication worksheet - I, Distributive property of multiplication worksheet - II, Writing and evaluating expressions worksheet, Nature of the roots of a quadratic equation worksheets, Determine if the relationship is proportional worksheet, Trigonometric ratios of some specific angles, Trigonometric ratios of some negative angles, Trigonometric ratios of 90 degree minus theta, Trigonometric ratios of 90 degree plus theta, Trigonometric ratios of 180 degree plus theta, Trigonometric ratios of 180 degree minus theta, Trigonometric ratios of 270 degree minus theta, Trigonometric ratios of 270 degree plus theta, Trigonometric ratios of angles greater than or equal to 360 degree, Trigonometric ratios of complementary angles, Trigonometric ratios of supplementary angles, Domain and range of trigonometric functions, Domain and range of inverse  trigonometric functions, Sum of the angle in a triangle is 180 degree, Different forms equations of straight lines, Word problems on direct variation and inverse variation, Complementary and supplementary angles word problems, Word problems on sum of the angles of a triangle is 180 degree, Domain and range of rational functions with holes, Converting repeating decimals in to fractions, Decimal representation of rational numbers, L.C.M method to solve time and work problems, Translating the word problems in to algebraic expressions, Remainder when 2 power 256 is divided by 17, Remainder when 17 power 23 is divided by 16, Sum of all three digit numbers divisible by 6, Sum of all three digit numbers divisible by 7, Sum of all three digit numbers divisible by 8, Sum of all three digit numbers formed using 1, 3, 4, Sum of all three four digit numbers formed with non zero digits, Sum of all three four digit numbers formed using 0, 1, 2, 3, Sum of all three four digit numbers formed using 1, 2, 5, 6, Solving Quadratic Equations Practice Problems, Solving Quadratic Equations Using the Quadratic Formula Worksheet, Apart from the stuff given in this section. If you want to learn how to find the inverse using the functions on a scientific calculator, keep reading the article! – Tuan Nguyen Feb 7 '11 at 14:31 Do not use the ^ button on your calculator to try entering A^-1 as separate keystrokes. If the determinant is 0, then your work is finished, because the matrix has no inverse. The decimals will automatically appear as fractions. How would I know if the inverse of a matrix does not exist? The matrix Y is called the inverse of X. I'm very satisfied. Your calculator probably has a function that will automatically convert the decimals to fractions. It means the matrix should have an equal number of rows and columns. No calculator, but I'm getting it, thanks to step-by-step, "I could not remember what my high school teacher taught me on how to find the inverse of a 3x3 matrix, so I got it, "Thank you very much. $\endgroup$ – poncho Sep 17 at 14:28 If the determinant is 0, the matrix has no inverse. A-1 exists. ", "The steps were clear and straightforward. In Part 1 we learn how to find the matrix of minors of a 3x3 matrix and its cofactor matrix. Thanks a lot! By using this service, some information may be shared with YouTube. A square matrix A has an inverse iff the determinant |A|!=0 (Lipschutz 1991, p. 45). This is an inverse operation. They are indicators of keeping (+) or reversing (-) whatever sign the number originally had. Find the inverse of the following matrix. The inverse of a matrix does not always exist. Are there any shortcuts for finding the inverse of a 3x3 matrix? This article has been viewed 3,487,721 times. ", "I now know how to find the inverse, finally! If the determinant of the matrix is zero, then the inverse does not exist and the matrix is singular. (2*2 - 7*4 = -24) Multiply by the chosen element of the 3x3 matrix.-24 * 5 = -120; Determine whether to multiply by -1. Thanks to all authors for creating a page that has been read 3,487,721 times. The adjugate matrix is noted as Adj(M). In our example, the matrix is () Find the determinant of this 2x2 matrix. So the determinant of C, of our matrix-- I'll do that same color-- … Just follow the steps; your determinant should be -2, and your matrix of co-factors should be (-1&1&1@1&1&1@2&2&0). Find the determinant of each of the 2x2 minor matrices, then create a matrix of cofactors using the results of the previous step. % of people told us that this article helped them. Once you do, you can see that if the matrix is a perfect identity matrix, then the inverse exists. Can you please help me find the answer to this problem? (Notice that in the formula we divide by det(M). For a given matrix A and its inverse A –1, we know we have A –1 A = I. Inverse of a matrix A is given by inv(A). https://www.mathsisfun.com/algebra/matrix-inverse-minors-cofactors-adjugate.html, http://www.mathcentre.ac.uk/resources/uploaded/sigma-matrices11-2009-1.pdf, http://www.mathwords.com/c/cofactor_matrix.htm, http://mathworld.wolfram.com/MatrixInverse.html, https://people.richland.edu/james/lecture/m116/matrices/inverses.html, consider supporting our work with a contribution to wikiHow, For a 3x3 matrix, find the determinant by first, To review finding the determinant of a matrix, see. To solve for the inverse of a 3x3 matrix, follow these steps • First, the matrix's determinant. For a more complete review, see. ", "Very good article. This post will explore several concepts related to the inverse of amatrix, i… Aninverse of a number is denoted with a −1superscript. Approved. ", "The method is understandable and really has the element of logic in it. Add to solve later Sponsored Links References Assuming that there is non-singular ( i.e. The final result of this step is called the adjugate matrix of the original. ", "Helped me in remembering how to find a 3x3 matrix. if you need any other stuff in math, please use our google custom search here. For example, if a problem requires you to divide by a fraction, you can more easily multiply by its reciprocal. To find the inverse of a 3x3 matrix, first calculate the determinant of the matrix. There are 18 references cited in this article, which can be found at the bottom of the page. then the matrix B is called an inverse of A. (You won’t always be so lucky.). ", "I was helped mainly with the formula of M^-1. The inverse of a number is its reciprocal. If you really can’t stand to see another ad again, then please consider supporting our work with a contribution to wikiHow. FINDING INVERSE OF 3X3 MATRIX EXAMPLES. Recall that the identity matrix is a special matrix with 1s in each position of the main diagonal from upper left to lower right, and 0s in all other positions. Since |A|  =  112 ≠ 0, it is non singular matrix. The calculator will find the inverse of the square matrix using the Gaussian elimination method, with steps shown. The inverse of a square matrix A, sometimes called a reciprocal matrix, is a matrix A^(-1) such that AA^(-1)=I, (1) where I is the identity matrix. Let A be an n x n matrix. The technique for inverting matrices is kind of clever. Courant and Hilbert (1989, p. 10) use the notation A^_ to denote the inverse matrix. ", "Thanks a lot for the detailed method you used to solve the problem. ", "This article really helped me. After that, you have to go through numerous lengthy steps, which are more time consuming in order to find the inverse of a matrix. A-1 exists. my matrix is implemented similar to your idea, the big matrix contains the pointers to the small matrices. For the sample matrix shown in the diagram, the determinant is 1. It is all simple arithmetic but there is a lot of it, so try not to make a mistake! Creating the Adjugate Matrix to Find the Inverse Matrix, {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/9\/97\/Find-the-Inverse-of-a-3x3-Matrix-Step-1-Version-2.jpg\/v4-460px-Find-the-Inverse-of-a-3x3-Matrix-Step-1-Version-2.jpg","bigUrl":"\/images\/thumb\/9\/97\/Find-the-Inverse-of-a-3x3-Matrix-Step-1-Version-2.jpg\/aid369563-v4-728px-Find-the-Inverse-of-a-3x3-Matrix-Step-1-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":"728","bigHeight":"546","licensing":"

License: Creative Commons<\/a>
\n<\/p>


\n<\/p><\/div>"}, {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/2\/2c\/Find-the-Inverse-of-a-3x3-Matrix-Step-2-Version-2.jpg\/v4-460px-Find-the-Inverse-of-a-3x3-Matrix-Step-2-Version-2.jpg","bigUrl":"\/images\/thumb\/2\/2c\/Find-the-Inverse-of-a-3x3-Matrix-Step-2-Version-2.jpg\/aid369563-v4-728px-Find-the-Inverse-of-a-3x3-Matrix-Step-2-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":"728","bigHeight":"546","licensing":"

License: Creative Commons<\/a>
\n<\/p>


\n<\/p><\/div>"}, {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/e\/ea\/Find-the-Inverse-of-a-3x3-Matrix-Step-3-Version-2.jpg\/v4-460px-Find-the-Inverse-of-a-3x3-Matrix-Step-3-Version-2.jpg","bigUrl":"\/images\/thumb\/e\/ea\/Find-the-Inverse-of-a-3x3-Matrix-Step-3-Version-2.jpg\/aid369563-v4-728px-Find-the-Inverse-of-a-3x3-Matrix-Step-3-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":"728","bigHeight":"546","licensing":"

License: Creative Commons<\/a>
\n<\/p>


\n<\/p><\/div>"}, {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/a\/a2\/Find-the-Inverse-of-a-3x3-Matrix-Step-4-Version-2.jpg\/v4-460px-Find-the-Inverse-of-a-3x3-Matrix-Step-4-Version-2.jpg","bigUrl":"\/images\/thumb\/a\/a2\/Find-the-Inverse-of-a-3x3-Matrix-Step-4-Version-2.jpg\/aid369563-v4-728px-Find-the-Inverse-of-a-3x3-Matrix-Step-4-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":"728","bigHeight":"546","licensing":"

License: Creative Commons<\/a>
\n<\/p>


\n<\/p><\/div>"}, {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/7\/7b\/Find-the-Inverse-of-a-3x3-Matrix-Step-5-Version-2.jpg\/v4-460px-Find-the-Inverse-of-a-3x3-Matrix-Step-5-Version-2.jpg","bigUrl":"\/images\/thumb\/7\/7b\/Find-the-Inverse-of-a-3x3-Matrix-Step-5-Version-2.jpg\/aid369563-v4-728px-Find-the-Inverse-of-a-3x3-Matrix-Step-5-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":"728","bigHeight":"546","licensing":"

License: Creative Commons<\/a>
\n<\/p>


\n<\/p><\/div>"}, Using Linear Row Reduction to Find the Inverse Matrix, {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/7\/74\/Find-the-Inverse-of-a-3x3-Matrix-Step-6-Version-2.jpg\/v4-460px-Find-the-Inverse-of-a-3x3-Matrix-Step-6-Version-2.jpg","bigUrl":"\/images\/thumb\/7\/74\/Find-the-Inverse-of-a-3x3-Matrix-Step-6-Version-2.jpg\/aid369563-v4-728px-Find-the-Inverse-of-a-3x3-Matrix-Step-6-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":"728","bigHeight":"546","licensing":"

License: Creative Commons<\/a>
\n<\/p>


\n<\/p><\/div>"}, {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/a\/aa\/Find-the-Inverse-of-a-3x3-Matrix-Step-7-Version-2.jpg\/v4-460px-Find-the-Inverse-of-a-3x3-Matrix-Step-7-Version-2.jpg","bigUrl":"\/images\/thumb\/a\/aa\/Find-the-Inverse-of-a-3x3-Matrix-Step-7-Version-2.jpg\/aid369563-v4-728px-Find-the-Inverse-of-a-3x3-Matrix-Step-7-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":"728","bigHeight":"546","licensing":"

License: Creative Commons<\/a>
\n<\/p>


\n<\/p><\/div>"}, {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/6\/61\/Find-the-Inverse-of-a-3x3-Matrix-Step-8-Version-2.jpg\/v4-460px-Find-the-Inverse-of-a-3x3-Matrix-Step-8-Version-2.jpg","bigUrl":"\/images\/thumb\/6\/61\/Find-the-Inverse-of-a-3x3-Matrix-Step-8-Version-2.jpg\/aid369563-v4-728px-Find-the-Inverse-of-a-3x3-Matrix-Step-8-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":"728","bigHeight":"546","licensing":"

License: Creative Commons<\/a>
\n<\/p>


\n<\/p><\/div>"}, {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/d\/da\/Find-the-Inverse-of-a-3x3-Matrix-Step-9.jpg\/v4-460px-Find-the-Inverse-of-a-3x3-Matrix-Step-9.jpg","bigUrl":"\/images\/thumb\/d\/da\/Find-the-Inverse-of-a-3x3-Matrix-Step-9.jpg\/aid369563-v4-728px-Find-the-Inverse-of-a-3x3-Matrix-Step-9.jpg","smallWidth":460,"smallHeight":345,"bigWidth":"728","bigHeight":"546","licensing":"

License: Creative Commons<\/a>
\n<\/p>


\n<\/p><\/div>"}, Using a Calculator to Find the Inverse Matrix, {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/0\/02\/Find-the-Inverse-of-a-3x3-Matrix-Step-10.jpg\/v4-460px-Find-the-Inverse-of-a-3x3-Matrix-Step-10.jpg","bigUrl":"\/images\/thumb\/0\/02\/Find-the-Inverse-of-a-3x3-Matrix-Step-10.jpg\/aid369563-v4-728px-Find-the-Inverse-of-a-3x3-Matrix-Step-10.jpg","smallWidth":460,"smallHeight":345,"bigWidth":"728","bigHeight":"546","licensing":"

License: Creative Commons<\/a>
\n<\/p>


\n<\/p><\/div>"}, {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/0\/08\/Find-the-Inverse-of-a-3x3-Matrix-Step-11.jpg\/v4-460px-Find-the-Inverse-of-a-3x3-Matrix-Step-11.jpg","bigUrl":"\/images\/thumb\/0\/08\/Find-the-Inverse-of-a-3x3-Matrix-Step-11.jpg\/aid369563-v4-728px-Find-the-Inverse-of-a-3x3-Matrix-Step-11.jpg","smallWidth":460,"smallHeight":345,"bigWidth":"728","bigHeight":"546","licensing":"

License: Creative Commons<\/a>
\n<\/p>


\n<\/p><\/div>"}, {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/a\/a6\/Find-the-Inverse-of-a-3x3-Matrix-Step-12.jpg\/v4-460px-Find-the-Inverse-of-a-3x3-Matrix-Step-12.jpg","bigUrl":"\/images\/thumb\/a\/a6\/Find-the-Inverse-of-a-3x3-Matrix-Step-12.jpg\/aid369563-v4-728px-Find-the-Inverse-of-a-3x3-Matrix-Step-12.jpg","smallWidth":460,"smallHeight":345,"bigWidth":"728","bigHeight":"546","licensing":"

License: Creative Commons<\/a>
\n<\/p>


\n<\/p><\/div>"}, {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/2\/25\/Find-the-Inverse-of-a-3x3-Matrix-Step-13.jpg\/v4-460px-Find-the-Inverse-of-a-3x3-Matrix-Step-13.jpg","bigUrl":"\/images\/thumb\/2\/25\/Find-the-Inverse-of-a-3x3-Matrix-Step-13.jpg\/aid369563-v4-728px-Find-the-Inverse-of-a-3x3-Matrix-Step-13.jpg","smallWidth":460,"smallHeight":345,"bigWidth":"728","bigHeight":"546","licensing":"

License: Creative Commons<\/a>
\n<\/p>


\n<\/p><\/div>"}, {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/7\/71\/Find-the-Inverse-of-a-3x3-Matrix-Step-14.jpg\/v4-460px-Find-the-Inverse-of-a-3x3-Matrix-Step-14.jpg","bigUrl":"\/images\/thumb\/7\/71\/Find-the-Inverse-of-a-3x3-Matrix-Step-14.jpg\/aid369563-v4-728px-Find-the-Inverse-of-a-3x3-Matrix-Step-14.jpg","smallWidth":460,"smallHeight":345,"bigWidth":"728","bigHeight":"546","licensing":"

License: Creative Commons<\/a>
\n<\/p>


\n<\/p><\/div>"}, {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/2\/2a\/Find-the-Inverse-of-a-3x3-Matrix-Step-15.jpg\/v4-460px-Find-the-Inverse-of-a-3x3-Matrix-Step-15.jpg","bigUrl":"\/images\/thumb\/2\/2a\/Find-the-Inverse-of-a-3x3-Matrix-Step-15.jpg\/aid369563-v4-728px-Find-the-Inverse-of-a-3x3-Matrix-Step-15.jpg","smallWidth":460,"smallHeight":345,"bigWidth":"728","bigHeight":"546","licensing":"

License: Creative Commons<\/a>
\n<\/p>


\n<\/p><\/div>"}, {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/d\/de\/Find-the-Inverse-of-a-3x3-Matrix-Step-16.jpg\/v4-460px-Find-the-Inverse-of-a-3x3-Matrix-Step-16.jpg","bigUrl":"\/images\/thumb\/d\/de\/Find-the-Inverse-of-a-3x3-Matrix-Step-16.jpg\/aid369563-v4-728px-Find-the-Inverse-of-a-3x3-Matrix-Step-16.jpg","smallWidth":460,"smallHeight":345,"bigWidth":"728","bigHeight":"546","licensing":"

License: Creative Commons<\/a>
\n<\/p>


\n<\/p><\/div>"}, {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/f\/fd\/Find-the-Inverse-of-a-3x3-Matrix-Step-17.jpg\/v4-460px-Find-the-Inverse-of-a-3x3-Matrix-Step-17.jpg","bigUrl":"\/images\/thumb\/f\/fd\/Find-the-Inverse-of-a-3x3-Matrix-Step-17.jpg\/aid369563-v4-728px-Find-the-Inverse-of-a-3x3-Matrix-Step-17.jpg","smallWidth":460,"smallHeight":345,"bigWidth":"728","bigHeight":"546","licensing":"