(a) A square matrix A is called idempotent if A² = A. Suppose that Xnxp(p < n) is a matrix such that XTX is invertible. Prove that both X(X¹X)-¹XT and In X(X¹X)-¹XT are idempotent. (Hint: use this property of matrix multiplication: (AB)C = A(BC)) (b) For X defined (a), prove the tr(X(X™X)−¹X¹) = p and tr(In - X(X¹X)-¹X¹) n-p =

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