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A1 Business and Technical College Linear Algebra Exercise

I’m working on a Mathematics question and need guidance to help me study.

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.)