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Math Help - Simple matrix algebra identity

  1. #1
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    Simple matrix algebra identity

    Hello everyone!

    I'm stuck on this particular concept...
    AB=AC \ \Rightarrow \ A(B-C)=0. Soooo when is it that B-C=0 i.e. B=C \ ... \ (1) but probably if A^{-1} exists then we can multiply to the right by A^{-1} so we get (1). But how can we know before hand?
    Thanks!
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  2. #2
    A Plied Mathematician
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    If you know that \det(A)\not=0, then A is invertible, which would imply that B=C. That's one condition that is sufficient. It's not necessary. As a counterexample, just let A=0, and B=C=I.

    Note: you're actually going to want to multiply on the left by A^{-1}, if it exists, in order to eliminate the A's.
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