Reference no: EM133246384

Linear Algebra Problem

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.)

If A is idempotent then we have to prove that (I-A)is idempotent:

b) It is given that A is invertible matrix so

c) Using the characteristics equation Ax=λx