A square matrix A is said to be idempotent if A2 = A. Let A be an idempotent matrix. (a) Show that I - A is also idempotent.
(b) Show that if A is invertible, then A = 1.
(C) Show that the only possible eigenvalues of A are 0 and 1. (Hint: Suppose x is an eigenvector with associated
eigenvalue and then multiply x on the left by A twice.)