Lesson Plan

Demonstrate with a specific example that matrix multiplication is not commutative: $AB \neq BA$ in general.

Verify that matrix multiplication is associative: $(AB)C = A(BC)$.

Apply the distributive properties: $A(B+C) = AB + AC$ and $(A+B)C = AC + BC$.

Recognize that $AB = O$ does not imply $A = O$ or $B = O$ (zero divisors exist in matrix algebra).

Explain why non-commutativity requires careful attention to the order of factors in matrix expressions.

HSN.VM.C.9