Attached is the question

Problem 2. (20 points.) Consider the (multiple) linear model (in the matrix notation) Y = X 5 + 6 (1) where X E MnX(P+1) (R), [3' E M(p+1)x1(lR), and e is an ndimensional random vector such that E(e) = 0 and COV(E) 2 021m where In is the n x n identity/unit matrix. Let H = X (X 'X )'1X " be the hat matrix. Verify that (In H) = (1,, H)