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Linear Algebra

  1. Feb 14, 2010 #1
    1. The problem statement, all variables and given/known data

    Prove: If A is an invertible matrix and k is a positive integer, then
    (A^k)^-1 = (A^-1)(A^-1) ....A^-1=(A^-1)^k

    2. Relevant equations
    none


    3. The attempt at a solution

    I have a hard time proving this. How do I go about doing this? Any help would be great. I really want to understand this. Thank you.
     
  2. jcsd
  3. Feb 15, 2010 #2

    vela

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    Just multiply [itex]A^k[/itex] by [itex](A^{-1})^k[/itex] and show you get the identity matrix.
     
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