Find the product AB, where 1 0 1 0-1 -1 1 0 a) A = -1 1 b) A = 1 2 -3 2 1 c) A = 0-1 7 2 -4 -3 Find a matrix A such that 2 B 01 4 -2 1 -1 0 0 1-1 2 3 2, B B = -1 03 -1 -3 -2 0 2 1 1 2 3 034 1 [Hint: Finding A requires that you solve systems of linear equations.] Let A = [1 Find a formula for A", whenever n is a positive integer. Show that (A)' = A. Let A and B be two nxn matrices. Show that a) (A + B) = A' + B. b) (AB) = B'A'. If A and B are nxn matrices with AB = BA = I, then B is called the inverse of A (this terminology is appropriate be- cause such a matrix B is unique) and A is said to be invertible. The notation B = A- denotes that B is the inverse of A.