[SOLVED] Abstract Algebra: Integers Modulo n 2

Hallo,

Me again. Here's the last of four questions I have for today. (I'll probably asking some questions about Set Theory soon, but not today).

Again, this is a homework problem, so please, only hints

__Problem:__

(a) Prove that if is even, then exactly one nonidentity element of is its own inverse.

(b) Prove that if is odd, then no nonidentity element of is its own inverse.

(c) Prove that equals either or in

(d) What does part (c) imply about modulo ?

__Things that might come in handy:__

Nothing really. Again, anyone who can help me will already know all they need to know by looking at the symbols and interpreting them.

__What I've tried:__

I honestly have not tried anything as yet. I don't think this is a particularly hard question. I remember being confused about something when I read it through the first time though, so I post it just in case, so as to not leave it for the last minute (which is when I usually do my homework).

I won't look at any hints given here until I've tried to do the problem myself (you can trust me :D). So feel free to respond anyway.

Thanks guys and gals!