Question: 1. For each of the following statements, either prove it or give a counterexample to the statement. [15 marks] (a) If A and D are

1. For each of the following statements, either prove it or give a counterexample to the statement. [15 marks] (a) If A and D are both invertible n x n matrices then so is ADAT. (b) If A2 = A and A =, 0 then A is invertible. (c) If A is an invertible n x n matrix. then the number of solutions of Ax = 1) depends on the vector b E R\". (d) If E is an elementary matrix then so is ET. (e) Let A and B be m x n matrices and D be an n x a matrix. If D is invertible and (A B)D = 0 then A = B

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