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Math Help - [SOLVED] Linear algebra matrix problem

  1. #1
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    [SOLVED] Linear algebra matrix problem

    If A, B, and C are all square matrices of the same size, show that AB commutes with C if A and B both commute with C.

    All I know is
    AC = CA
    BC = CB

    But I don't know what to do with that information to prove this.
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  2. #2
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    Quote Originally Posted by paulrb View Post
    If A, B, and C are all square matrices of the same size, show that AB commutes with C if A and B both commute with C.

    All I know is
    AC = CA
    BC = CB

    But I don't know what to do with that information to prove this.
    Since AC = CA\;\;\Rightarrow\;\;ACB = CAB\;\;\Rightarrow\;\; ABC=CAB.
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  3. #3
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    Thanks, that's a lot easier than I thought. I guess I was thinking too hard.
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