Which Rules Work for Matrix Multiplication? For each of Problems 1-3, prove the statement in general or give a counterexample. In each problem, A, B, and I denote n x n matrices, and x̅, Y̅. and z̅ denote column vectors in Rn . For the proofs, use the properties of matrix multiplication and do not break the matrices down into elements.
1. (A + B) (A-B) = A2 - B2
2. (A+B)2 = A2 + 2AB + B2
3. (l + A)2 = l + 2A + A2