1. The problem statement, all variables and given/known data(adsbygoogle = window.adsbygoogle || []).push({});

Let A and B be (2x2) matrices such that A^2 = AB and A does not equal the zero matrix O. Find the flaw in the following proof that A = B:

Since A^2 = AB, A^2 - AB = the zero matrix O

Factoring yields A(A-B) = O

Since A does not equal O, it follows that A - B = O.

Therefore, A = B.

3. The attempt at a solution

I tried setting up two matrices A and B where A = [ a b, c d] and B = [ e f, g h] and following through on the steps of the proof to see if each of the statements was true. However, I kept finding that they were all true.

Please help.

Thanks.

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# Homework Help: Algebraic Properties of Matrix Operations

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