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Help with a simple matrix proof

  1. Feb 23, 2009 #1
    Edit: Sorry, I figured this out shortly after posting. It's a simple problem but I hadn't used matrix equations before.

    1. The problem statement, all variables and given/known data

    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.

    2. Relevant equations

    Formula for matrix multiplication

    3. The attempt at a solution

    All I know is
    AC = CA
    BC = CB
    A, B, and C are square matrices of the same size

    I want to prove that (AB)(C) = (C)(AB).
    But I am not sure how to do this, or even how to get started.
  2. jcsd
  3. Feb 23, 2009 #2
    Well Matrix multiplication is associative so you should be able to manipulate (AB)C to get C(AB) pretty easily.
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