Understand matrix multiplication properties

What you'll learn

1. Demonstrate with a specific example that matrix multiplication is not commutative: $AB \neq BA$ in general.
2. Verify that matrix multiplication is associative: $(AB)C = A(BC)$.
3. Apply the distributive properties: $A(B+C) = AB + AC$ and $(A+B)C = AC + BC$.
4. Recognize that $AB = O$ does not imply $A = O$ or $B = O$ (zero divisors exist in matrix algebra).
5. Explain why non-commutativity requires careful attention to the order of factors in matrix expressions.

Prerequisites

• Add, subtract, and multiply matrices