Question: Let P = A(ATA)-1 AT, where A is an m n matrix of rank /;. (a) Show that P2 = P. (b) Prove Pk

Let P = A(ATA)-1 AT, where A is an m × n matrix of rank /;.
(a) Show that P2 = P.
(b) Prove Pk = P for k = 1,2
(c) Show that P is symmetric. [If B is nonsingular, then (B-1)T = (BT)-1]

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