Question

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 = I.

(c) Show that the only possible eigenvalues of A are 0 and 1. (Hint: Suppose x is an eigenvector with associated eigenvalue λ and then multiply x on the left by A twice.)​

Answer 1

Answer:

answer of part (a) is given above