   Chapter 1.6, Problem 26E

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Textbook Problem
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# Let A and B be square matrices of order n over ℝ . Prove or disprove that if A B is a diagonal matrix of order n over ℝ , then at least one of A or B is a diagonal matrix.

To determine

Whether if AB is a diagonal matrix of order n over , then at least one of A or B is a diagonal matrix.

Explanation

Given information:

A and B be square matrices of order n over .

Formula used:

Definition: Matrix multiplication

The product of m×n matrix A over and n×p matrix B over is m×p matrix C=AB, where the element cij in row i and column j of AB is found by using the elements in row i of A, and the elements in column j of B in the following manner:

columnjofBcolumnjofCrowiofA[ai1ai2ai3ain][b1jb2jb3jbnj]=[

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