1. 2.2 The Inverse of a Matrix

2. Example: REVIEW

3. Invertible (Nonsingular)

4. Theorem 4 Example:

5. Theorem 5 Proof: Example: Use the inverse of the matrix to solve the system

6. Theorem 6 1. If is an invertible matrix, then is invertible: 2. If and are invertible matrices, then so is : 3. If is an invertible matrix, then so is :

7. Elementary Matrix obtained by performing a single elementary row operation on an identity matrix. Example:

8. Remark

9. Theorem 7

10. How to find : Example: Find the inverse of