Download Article Show Download Article Struggling with a tough algebra problem? Finding the inverse of a matrix is key to solving systems of linear equations. Plus, inverse operations provide an easy way to simplify difficult problems in general. For example, if a problem asks you to divide by a fraction, you can more easily multiply by its reciprocal. That’s a basic inverse operation! Similarly, since there's no division operator for matrices, you need to multiply by the inverse matrix. We’ve put together a step-by-step guide to calculating the inverse of a 3x3 matrix by hand, using determinants and linear row reduction. Then, we’ll even teach you how to find the inverse with an advanced graphing calculator.
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ReferencesAbout This ArticleArticle SummaryX To find the inverse of a 3x3 matrix, first calculate the determinant of the matrix. If the determinant is 0, the matrix has no inverse. 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. Find the determinant of each of the 2x2 minor matrices, then create a matrix of cofactors using the results of the previous step. Divide each term of the adjugate matrix by the determinant to get the inverse. If you want to learn how to find the inverse using the functions on a scientific calculator, keep reading the article! Did this summary help you? Thanks to all authors for creating a page that has been read 4,044,725 times. Reader Success Stories
Did this article help you?How do you find the inverse of a 3x3 matrix?For finding the inverse of a 3x3 matrix (A ) by elementary row operations,. Write A and I (identity matrix of same order) in a single matrix separating them by a vertical dotted line.. Apply elementary row operations so that the left side matrix becomes I.. The matrix that comes on the right side is A-1.. How do you solve a system of equations using an inverse matrix?SOLVING A SYSTEM OF EQUATIONS USING THE INVERSE OF A MATRIX. Given a system of equations, write the coefficient matrix A, the variable matrix X, and the constant matrix B. Then.. Multiply both sides by the inverse of A to obtain the solution.. Do all 3x3 matrices have an inverse?A 3 x 3 matrix has 3 rows and 3 columns. Elements of the matrix are the numbers that make up the matrix. A singular matrix is the one in which the determinant is not equal to zero. For every m×m square matrix there exist an inverse of it.
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