Simple Group Theory Questions

Hi,
I'm self-studying group theory, and I couldn't solve a few of the
exercises.
Any hints on how to get them is highly appreciated.
The questions are:

1- Let G be a group such that for all x in G, x^2=e (e being the
identity element). Prove G is abelian.

2- Let S be a set and / an operation that assigns to each ordered pair
(a,b) an element a/b of S, such that:
a. there is an element a in S such that a/b=1 if and only if a=b;
b. for any elements a,b,c in S, (a/b)/(b/c)=(a/b)
Prove that S is a group under the product defined by ab=(a/(1/b)).

I'd prefer some simple hints on how to approach them, rather than
complete proofs, because i'd like to solve them myself.

Thanks a lot.

.

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