I need help with the following problems:
32. Find a formula for det (rA) when A is an n x n matrix and r is a scalar.
34. Let A and P be square matrices, with P invertible. Show that det [PA(P^-1)] = det A.
45. Suppose that all the entries in A are integers and det A = 1. Explain why all the entries in A^-1 are integers.