Question: (20) We say a matrix A E 63 is idempotent it A2 = A. {3) Prove by induction that if A is idempotent, then A

(20) We say a matrix A E 63\"" is idempotent it A2 = A. {3) Prove by induction that if A is idempotent, then A" = A for all positive integers k. {b) Prove that the only invertible idempotent matrix is the identity matrix. to) Prove that A is idempotent if and only if i 2A is invertible and is its own inverse

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