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Algebraic Properties of Matrix Operations

  1. Jan 19, 2010 #1
    1. The problem statement, all variables and given/known data

    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.
  2. jcsd
  3. Jan 19, 2010 #2


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    Can you find two 2x2 matrices D and E such that DE=0 and neither D nor E is 0? That would be a flaw, wouldn't it?
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