Which Rules Work for Matrix Multiplication? For the Problem, prove the statement in genera...

Which Rules Work for Matrix Multiplication? For the Problem, prove the statement in general or give a counterexample. In each problem, A, B, and I denote n × n matrices, and , , and denote column vectors in ℝn. HINT: For the proofs, use the properties of matrix multiplication and do not break the matrices down into elements.

(A + B)(A − B) = A2 − B2