How to Find the Inverse of a Matrix

Step-by-Step Guide

1. 1

   Step 1: Make sure your matrix is square.

   A matrix can have an inverse matrix only if its number of columns is equal to its number of rows.
   
   If your matrix is not square, there is no inverse. , If your matrix has 2 rows and 2 columns, you can find its inverse directly with this method.
   
   If your matrix has 3 or more rows and 3 or more columns, use Method
   2., To find the multiplicative inverse of a 2x2 matrix, use the above formula., Let arc be the element in the matrix at the rth row and the cth column.
   
   Its cofactor Arc will then be (-1)r+c det (arc), where det (arc) is the determinant of 2x2 matrix formed by skipping the rth row and the cth column, in which element arc lies.
   
   The determinant of a general 2x2 matrix looks like above., A determinant is a particular number that can be calculated from any square matrix.
   
   It is typically denoted with vertical bars, just like an absolute value.
   
   Add the cofactors of the elements in the first row of the matrix to find the determinant., If the determinant is 0, there is no inverse matrix., The inverse of a 2x2 matrix is simple, as you can see above: simply switch the positions of a and d, place negatives in front of b and c, and divide all by the determinant.
   
   To see how this works in a more complicated example, see Method
   2.
2. 2

   Step 2: Check whether your matrix is 2x2.

3. 3

   Step 3: Know your formula.

4. 4

   Step 4: Calculate cofactors.

5. 5

   Step 5: Find the determinant of the matrix.

6. 6

   Step 6: Check whether the determinant is 0.

7. 7

   Step 7: Find your inverse matrix.

Detailed Guide

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