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

detail proof

7. Let A be a square matrix so that AB = If A for every square matrix B of the same order. (6] () Prove that A is a diagonal matrix. [ Hint: Let # be the matrix whose (i, i)-entry is I and D chewhere. Prove that ay - 0 whenever i # j-1 (il] Prove that A is a scalar matrix. [Hinr. For f # j, let B be the matrix whose (i, j)-entry is I and O elsewhere, Prove that ay = ajj.l

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