Question: Upper Triangular Matrices A square n ( n matrix A = [aij] is called upper triangular if aij = 0 for i > j. (All

Upper Triangular Matrices A square n ( n matrix A = [aij] is called upper triangular if aij = 0 for i > j. (All entries below the main diagonal are zero.)
(a) Give three examples of upper triangular matrices of different orders.
(b) For the 3 ( 3 case, prove that if A and B are both upper triangular, then AB is also upper triangular.
(c) Prove part (b) for the general case (arbitrary n).

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