Question: 1. For any n x n matrices A and B, we define [A, B] = AB - BA. (a) Let A = (aij)3x3, where aij

1. For any n x n matrices A and B, we define [A, B] = AB - BA. (a) Let A = (aij)3x3, where aij = i + j - 2; j-i ifi j. (i) Write down A and B explicitly. (ii) Compute [A, B]. (b) For any n x n matrices A, B and C, show that [A + B, C] = [A, C] + [B, C] and [A, B] = -[B, A]. (c) Let A = ( ?) Find all 2 x 2 matrices X such that [A, X] = 0. a b (Hint: Write X = d and compute [A, X].)

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