Help. I feel like i'm over complicating this in my head.
Let G be a group, and let a be in G. Prove that C(a)=C(a^-1).
I'm struggling with getting to show that. It's given that ag=ga and a^1g=ga^1.
I tried to go with
a^1 g a
= g a^1 a
= g e
and: a g a^1
= g a a^1
= g e
so a a^1 = a^1 a But I feel I'm making assumptions somewhere so the proof doesn't hold. I'm so lost! Thanks for your reply, it makes sense, I'm just not sure how to show what you're saying...