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Homework Help: Group theory. Help

  1. Feb 18, 2010 #1
    1. The problem statement, all variables and given/known data

    Let G(*) be a group.
    If x.y are elements of G show that (x*y*z^-1)^-1 = x*y^-1*x^-1

    2. Relevant equations

    3. The attempt at a solution
    I first took the left side of the equation and computed the inverse and I got x^-1*y^-1*z
    I then let this equal to the righthand side and concluded since the elements are in a group the associativity law holds they are equal. I was just wondering is this valid or am I missing something.
  2. jcsd
  3. Feb 18, 2010 #2
    I think the right side should be zy-1x-1, not xy-1x-1.
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