Question: Please answer in detail. 3.86 Let Q and D be n x n matrices with Q invertible. a. / Prove that (Q-1DQ)2 = Q-1D2Q. Warning:

Please answer in detail.

3.86 Let Q and D be n x n matrices with Q invertible. a. / Prove that (Q-1DQ)2 = Q-1D2Q. Warning: Matrix multiplication is not necessarily commutative! It is not usually true thatQ- 1DQ = D.It is also not in general true that for matrices(AB)2 = A2B2. (See Exercise 3.85.) b. What is the corresponding formula for (Q- 1DQ)3? (Q-1DQ)"? Prove your answer. 3.87 Compute a formula for A", where A = 3 Suggestion: Show that A = QDQ- 1 where Q = D= O ON 4 Then use the result from Exercise 3.86

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