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I have quastion about groups:

G is abelian group with an identity element "e".

If xx=e then x=e.

Is it true or false?

I was thinking and my feeling is that it's true but I just can't prove it.

I started with:

(*) ae=ea=a

(*) aa^-1 = a^-1 a = e

those from the definition of Group

and now the assuming: aa=e

then:

aa^-1 = e = aa

a=a^-1

==> a^-1 a = aa = e

that's all i got.

Is anyone can halp?

thank you!

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# Homework Help: Quastion about abelian group

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