1. Section 9.6 Determinants and Inverses Objectives To understand how to find a determinant of a 2x2 matrix. To understand the identity matrix. Do define and compute the inverse of a matrix.

2. Determinants If a matrix is a square matrix, then it can be assigned a number called its determinant. The determinant is denoted by det(A) or.

3. The determinant of the 2 x 2 matrix is:

4. Ex 1. Find the determinant of A.

5. Class Work Find the determinant of A and B. 1. 2.

6. The Identity Matrix The identity matrix, I, is the n x n matrix for which each main diagonal entry is a 1 and for which all other entries are 0.

7. Identity matrices behave like the number 1 in the sense that A · I n = A and I n · B = B whenever these products are defined.

8. Inverse of a Matrix. Let A be a square n x n matrix. If there exists an n x n matrix A –1 with the property that AA –1 = A –1 A = I n then we say that A –1 is the inverse of A.

9. Ex 2. Verify that B is the inverse of A.

10. Class Work 3. Verify that B is the inverse of A.

11. Finding the inverse of a 2x2 matrix. If and det(A) ≠ 0, then

12. Ex 3. Find.

13. Ex 4. Find.

14. Class Work Find the inverse of A. 4.5. 6.

15. Inverse Worksheet 1-15