Multiply it to the right by (ab)

Since it is a group, * is associative.

So we can write :

So we have

Therefore...

Abelian means that * is commutative.b) A group G is Abelian iff (ab)^-1=a^-1 * b^-1

If it is Abelian, by the previous relation.

If , then since , we have

Thus it is commutative --> Abelian

The equivalence is proved.

c) In a group (a^-1)^-1=a for all a

Sorry for the wording & the method... just trying myself to explain