Thread: Beginning 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

Originally Posted by jzellt

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

Obviously, you need a counterexample to . - What about with multiplication?

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!