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13.5 P ROPERTIES OF M ATRIX M ULTIPLICATION

W ARM -U P Use the following matrices to find 1 and 2 and 1. AB 2. BA

What did you find about #1 and #2? So, we can say that matrix multiplication is not. The only matrix where order doesn’t matter when you multiply is called the matrix. they are not equal commutative identity

L ET, SIMPLIFY : 3. 4.

What did you find when you multiplied matrix A by the identity matrix? So, no matter which way you multiply the identity ( left or right ), you get the same answer! you get matrix A both times

P ROPERTIES OF M ATRIX M ULTIPLICATION FOR 2X2 M ATRICES Let A, B, and C be 2X2 matrices and a be a scalar: 1.Closure Property: 2.Associative Property: 3.Distributive Property: 4.Identity Property: 5.Associative Property for Scalar: 6.Multiplicative Property of Zero Matrix:

U SE THE FOLLOWING TO SHOW #5 5.

U SE THE FOLLOWING TO SHOW #6 6.

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