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Group problem

  1. Dec 17, 2013 #1
    1. The problem statement, all variables and given/known data
    Find ##(g_ig_j)^{-1}## for any two elements of group ##G##.



    2. Relevant equations
    For matrices ##(AB)^{-1}=B^{-1}A^{-1}##



    3. The attempt at a solution
    I'm not sure how to show this? I could show that for matrices ##(AB)^{-1}=B^{-1}A^{-1}##. And that for numbers
    ##(ab)^{-1}=a^{-1}b^{-1}##
     
  2. jcsd
  3. Dec 17, 2013 #2

    tiny-tim

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    Hi LagrangeEuler! :smile:
    If h = ##(g_ig_j)^{-1}##, then ##hg_ig_j## = I.

    Sooo what combinations of gs would h have to be made of? :wink:
     
  4. Dec 17, 2013 #3
    Could I just write from that relation that ##(g_ig_j)^{-1}=g_j^{-1}g_i^{-1}##? :)
    It looks obvious but what is right mathematical way to write it? :)
     
  5. Dec 17, 2013 #4

    jbunniii

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    Check whether it satisfies the properties of the inverse. If ##h## is the inverse of ##g##, then ##hg = gh = 1##. See if your ##h## satisfies this for ##g = g_i g_j##.
     
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