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.

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.

The determinant of the 2 x 2 matrix is:

Ex 1. Find the determinant of A.

Class Work Find the determinant of A and B

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.

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.

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.

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

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

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

Ex 3. Find.

Ex 4. Find.

Class Work Find the inverse of A

Inverse Worksheet 1-15