Prove this is true for every group G, or give a counter example to show this is false in some groups:

If x^2 = a^2, then x=a

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- September 17th 2010, 10:07 PMjzelltBeginning Abstract Algebra Problem
Prove this is true for every group G, or give a counter example to show this is false in some groups:

If x^2 = a^2, then x=a - September 17th 2010, 10:35 PMFailure
- September 18th 2010, 07:13 AMHallsofIvy
Another, simpler, example is the set {1, -1} with multiplication as operation. Yet, another, the Klein 4-group. In fact, any finite group whose order is even!