о 6. (a) Let A, B be square matrices over F and suppose there exist rect- angular matrices P, Q such that A = PQ and B =
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о 6. (a) Let A, B be square matrices over F and suppose there exist rect- angular matrices P, Q such that A = PQ and B = QP. If h(x) E P(F), prove that Ah(A) = Ph(B)Q. Hence show that AmB(A) = 0 = BmA(B). Deduce that one of the following holds: mA(x) = mB(), mA(2) = rmb(x), mb(I) = rmA() (b) Express the n x n matrix 1 1 1 2 2 : n п n a as the product of a column matrix and a row matrix. Hence find its minimal polynomial.