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Proof about identity element of a group

  1. Sep 4, 2012 #1
    1. The problem statement, all variables and given/known data
    If G is a group, a is in G, and a*b=b for some b in G (* is a certain operation), prove that a is the identity element of G


    2. Relevant equations



    3. The attempt at a solution
    I feel like you should assume a is not the identity element and eventually show that a= the identity. but im not sure how to show that.
     
  2. jcsd
  3. Sep 4, 2012 #2

    LCKurtz

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    Hint: Think about using ##b^{-1}##.
     
  4. Sep 4, 2012 #3
    I thought about using the inverse of b but i'm not sure how to plug it in?
     
  5. Sep 4, 2012 #4

    LCKurtz

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    You don't "plug it in". You could try *-ing things with it.
     
  6. Sep 4, 2012 #5
    Could you do a*b*b-inverse=b*b-inverse? and go from there?
     
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