Question

Theorem 1.2 Properties of Matrix Multiplication

(a) If A, B, and C are matrices of the appropriate sizes, then
A(BC) = (AB)С.
(b) If A, B, and C are matrices of the appropriate sizes, then
(A+B)CAC + BC.
(c) If A, B, and C are matrices of the appropriate sizes, then
C(A+B) = CA+CB.

Answer 1

The properties of matrix multiplication are associative, distributive, and commutative.

Step-by-step explanation:

The given Theorem 1.2 states the properties of matrix multiplication:

• (a) If A, B, and C are matrices of the appropriate sizes, then A(BC) = (AB)C.
• (b) If A, B, and C are matrices of the appropriate sizes, then (A+B)CAC + BC.
• (c) If A, B, and C are matrices of the appropriate sizes, then C(A+B) = CA+CB.

These properties demonstrate the associative, distributive, and commutative properties of matrix multiplication.