Matrix laws and counterexamples

Explore matrix laws through proofs, counterexamples and carefully stated assumptions. This precalculus extension practice covers compatible dimensions, associativity, cancellation, zero products and the reverse order of inverses. Single-select and multiselect problems progress from checking a claim to explaining exactly why it holds or fails. Worked explanations distinguish a successful numerical example from a general argument and show why familiar scalar rules cannot be transferred blindly to matrices. Basic matrix multiplication and introductory proof vocabulary are prerequisites.