Prove that if A and B are diagonal matrices (of the same size), then AB = BA. Getting Started: To prove that the matrices AB and BA are equal, you need to show that their corresponding entries are equal. (i) Begin your proof by letting A = [aj] and B = [bj] be two diagonal nx n matrices. (ii) The ijth entry of the product AB is Cij k = 1 (iii) Evaluate the entries cj for the two cases i +j and i = j. Cij if i + j Cji = otherwise (iv) Repeat this analysis for the product BA. Find the ijth entry of the product BA. dij = L ajkbki k = 1 O dij = ajkbki k = 1 dij = bikaki k = 1 -Σ |O dij = bjkāki k = 1

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