# The inverse of 3 x 3 matrices with matrix row operations - Matrices

### The inverse of 3 x 3 matrices with matrix row operations

In this section, you will learn how to find the inverse of a 3 x 3 matrix. This method requires the use of matrix row operation. The idea is to draw a vertical line in the middle, write the matrix on the left side of the line, and write the 3 x 3 identity matrix on the right side of the line. Then the goal is to do a bunch of matrix row operation so that the identity matrix appears on the left side of the line. Whatever appears on the right side will be the inverse. Note that this method works for 2 x 2 matrices as well, except the right side of the line is a 2 x 2 identity matrix.

###### Basic concepts:

- The three types of matrix row operations
- Solving a linear system with matrices using Gaussian elimination
- Identity matrix

###### Related concepts:

- The inverse of 3 x 3 matrix with determinants and adjugate