(20 pts) Given an n x n matrix A with real entries such that 4% = 1I, prove the following statements about A. (a) A is invertible. (b) A has no real eigenvalues, and exactly two complex eigenvalues which are *u. () n is even. (d) det(A) =1. (e) Show that A is diagonalizable. (this is quite a bit harder than the rest of the set)