Let G be a multiplicatively-written group with exactly two elements e and a, where e is the identity element. Prove that a^2=e.

My proof: since there are only elements e and a, it means that a=a^(-1). e=a*a^(-1)=a*a=a^2

Logically that's probably fine, but can this be considered a correct proof?

Question

Let G be a multiplicatively-written group with exactly two elements e and a, where e is the identity element. Prove that a^2=e.

My proof: since there are only elements e and a, it means that a=a^(-1). e=a*a^(-1)=a*a=a^2

Logically that's probably fine, but can this be considered a correct proof?

perl · Answer

proof: 
if a = e, then e^2 = e*e = e , and you are done.

it might be easier to show this with a cayley table

perl · Answer

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