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A square matrix A is said to be idempotent if A2 = A. Let A...

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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 A and then multiply x on the left by A twice.)

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