Question: (2) Let A and B be n x n-matrices. Your good friend Fred R. Dimm believes that det AB B = det(A + B) det(A

(2) Let A and B be n x n-matrices. Your good friend Fred R. Dimm believes that det AB B = det(A + B) det(A - B). He offers the following argument to support this claim: det AB B = det(A2 - B2) = det [(A + B)(A - B)] = det(A + B) det(A - B) . (a) Comment (helpfully) on his "proof". In particular, explain carefully why each of the three steps in his "proof" is correct or incorrect. (That is, provide a proof or a counterexample to each step.) (b) Is the result he is trying to prove actually true? Hint: Consider the product B A+BO A - B 0

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