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Proof about identity element of a group

  • Thread starter hoopsmax25
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  • #1
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Homework Statement


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


Homework Equations





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.
 

Answers and Replies

  • #2
LCKurtz
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Hint: Think about using ##b^{-1}##.
 
  • #3
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I thought about using the inverse of b but i'm not sure how to plug it in?
 
  • #4
LCKurtz
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You don't "plug it in". You could try *-ing things with it.
 
  • #5
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Could you do a*b*b-inverse=b*b-inverse? and go from there?
 

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