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Math Help - Matrix Power

  1. #1
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    Matrix Power

    If AB = BA and p is a nonnegative integer, prove that (AB)^ p = A^p B^p.

    I've been sitting on this one for an hour and I'm just ridiculously confused!
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  2. #2
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    Quote Originally Posted by Brokescholar View Post
    If AB = BA and p is a nonnegative integer, prove that (AB)^ p = A^p B^p.

    I've been sitting on this one for an hour and I'm just ridiculously confused!
    by induction over p. if p = 1 it's clear. assuming it's true for p, then: (AB)^{p+1}=A(BA)^pB=A(AB)^pB=A(A^pB^p)B=A^{p+1}B^{  p+1}. \ \ \ \square
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  3. #3
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    Awesome! You're a genius thanks for the help!
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