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Please help me solve question 4 4. (a) Find a 3 x 3 matrix A # 0 such that A2 # 0, but A3 =

Please help me solve question 4

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4. (a) Find a 3 x 3 matrix A # 0 such that A2 # 0, but A3 = 0. (b) Show that if B is an n x n matrix such that B* = 0 for some natural number k, then B is not invertible. (Remark: Part (a) reminds us that if B* = 0 it need not be the case that B = 0.) 5. Let P and Q be 5 x 5 matrices such that det (P) = 2 and det(Q) = -3

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