Question: detail proof 7. Let A be a square matrix so that A B = BA for every square matrix B of the same order. (6]

detail proof

7. Let A be a square matrix so that A B = BA for every square matrix B of the same order. (6] (i) Prove that A is a diagonal matrix. [Hint: Let B be the matrix whose (i, i)-entry is I and 0 elsewhere. Prove that ajj = 0 whenever i / j.] (ii) Prove that A is a scalar matrix. [Hint. For i # j, let B be the matrix whose (i, j)-entry is 1 and 0 elsewhere. Prove that aji = ajj.l

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