1. Inverses of n x n Matrices

2. The Inverse Matrix If A is an n x n matrix, the inverse of A (call it A -1 ) is the matrix such that A * A -1 is equal to the n x n identity matrix, I n.

3. Calculating the Inverse Matrix Here are the steps you can use to find the inverse of a matrix: 1. Augment your matrix with the identity matrix. 2. Use Gauss-Jordan elimination to put your matrix in reduced row echelon form. 3. The “identity matrix” side of your augmented matrix is the inverse of your original matrix. Basically, you start with the matrix on the left and the identity matrix on the right, and you end with the inverse matrix on the right and the identity matrix on the left. This works for square matrices of any size.

4. Example

5. Solution First, we augment our matrix with the identity matrix. The resulting augmented matrix is

6. Solution