1. Identity and Inverse Matrices

2. The Identity Matrix
The identity matrix [I] for multiplication is a square matrix with a 1 for every element of the principal diagonal (top left to bottom right) and a 0 in all other positions.
Example: 3x3 Identity Matrix

3. Identity Matrix
A I = A
A =

4. Inverse Matrix
The product of a matrix and its inverse is the identity matrix.
A-1 is the notation to designate the inverse of a matrix.
A A-1 = I

5. Since XY≠I, they are not inverses!
Verify Inverse Matrices: Determine whether the pair of matrices are inverses.
Since XY≠I, they are not inverses!

6. Find the inverse of the matrix.
Step 1: Find the determinant.
Step 2: Multiply by

7. Find the inverse of the matrix.
Step 1: Find the determinant.
Step 2: Change the matrix:
Step 3: Multiply by

8. Find the inverse of each matrix.
Step 1: Find the determinant of the matrix.
Since the determinant equals 0, R-1 does not exist.