Lesson 4: Inverses of Matrices (part 1) Accel Precalc Unit #3: Matrices Lesson 4: Inverses of Matrices (part 1) EQ: How do you algebraically determine if a pair of matrices are inverses?

Dimensions are m x m All entries are 0 Part I: Defining Inverse Matrices Terms to Recall: Dimensions are m x m Square Matrix All entries are 0 Zero Matrix

What do you notice about each product? Ex 1. Multiply. a) b) What do you notice about each product? product equals first matrix

Identity Matrix What name can we give a matrix in the form Multiplication by the identity matrix allows a matrix to keep its identity. What are the characteristics of this matrix? Square matrix 1’s down the diagonal & 0’s everywhere else

When a given square matrix, A, is multiplied by the identity matrix, I, the matrix A keeps its values (its identity). Therefore AI = A = IA

Ex. 2 Multiply a) Let Find AB Find MN b) Let

What was the product matrix for AB and MN? RECALL: The product of multiplicative inverses is 1. Two matrices are inverses of each other if their product is the identity matrix.

Ex. 3 Determine if each pair of matrices are inverses of each other. a) b)

ASSIGNMENT: Practice Worksheet 4.3 #1 – 6 On another sheet of paper, algebraically prove if the given matrices are inverses of each other.