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1. Homework Statement
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.
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.