Question: Problem 3 For any two matrices A, B E Rmxn, define inner product (A, B) := Tr (ATB) (a) Show that (A, B) = >;;

Problem 3 For any two matrices A, B E Rmxn, define inner product (A, B) := Tr (ATB) (a) Show that (A, B) = >;; aijbij, for A = [adj], B = [buj]. (b) Let V = {A E Rnxn : A is symmetric), W = {B ERnxn : B is skew-symmetric}. Show that V = WI. Hint: use the fact that Tr (AB) = Tr (BA)

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