5) a) Suppose matrix A is idempotent. Show that A' must also be idempotent. b) Let...

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5) a) Suppose matrix A is idempotent. Show that A must also be idempotent. b) Let A be an arbitrary 2x2 matrix. Show that the matrix AA is symmetric (Again, to prove these results you cannot use specific examples.) 6) Let B I-A(AA) A. a) Must B be square? Must A be square? Must (AA) be square? b) Show that matrix B is idempotent. (Once again, do not use specific examples.)

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