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An Abelian Group Problem

  • Thread starter e(ho0n3
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[SOLVED] An Abelian Group Problem

Homework Statement
Prove: If G is a group where the square of every element equals the identity element, then G is Abelian.

The attempt at a solution
I've been able to prove is that a-1 = a and that (ab)-1 = ba where a and b are in G. Everything else I've done leads into a dead-end. Any tips?
 

Answers and Replies

  • #2
HallsofIvy
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Okay, you know that a-1= a for every element of the group (including ab) and you know that (ab)-1= ba. What do those two together tell you?
 
  • #3
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I see now! Boy do I feel stupid. Thanks.
 
  • #4
HallsofIvy
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Hey, feeling stupid is the beginning of learning!
 

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