Proving a = a^-1 implies a^2 = e in group theory

[mehrts]

Let G be a group. Let 'a' be an element of G. Let e be the identity of G Prove that if a = a^-1 then a^2= e.

Is the proof below correct ?
Suppose a = a^-1. Then

a^2 = aa = a(a^-1) = e.

 

[buzzmath]

yeah, if a is it's own inverse then a^2 is e. your proof looks fine to me.

 

[mehrts]

Thxs. He he he :!)