Guided Proof Prove that if A and B are diagonalmatrices
Chapter 2, Problem 2.1.61(choose chapter or problem)
Guided Proof Prove that if A and B are diagonalmatrices (of the same size), then AB = BA. Getting Started: To prove that the matrices AB and BAare equal, you need to show that their correspondingentries are equal.(i) Begin your proof by letting A = [aij] and B = [bij]be two diagonal n n matrices.(ii) The ijth entry of the product AB iscij = nk=1aikbkj.(iii) Evaluate the entries cij for the two cases i j andi = j.(iv) Repeat this analysis for the product BA
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