Homomorphism abelian help

Homework Statement

Prove that Group G is abelian iff the function f:G to G given by f(a)=a^-1 is a homomorphism

The Attempt at a Solution

Group G must be communitative for it to be abelian I have no idea where to start to begin to prove this I know that homomorphic means that complete the operation first on a in the group gets mapped to an element that the operation is completed 2nd. Help... I really need a jumping point.

StatusX
Homework Helper
You can start by writing out some relevant definitions and basic facts along with the facts you're given. Often this is also where you finish. In this case, remember that the condition for f to be a homomorphism is f(ab)=f(a)f(b). Now use the definition of f.

Last edited:
matt grime
Homework Helper
Group G must be communitative for it to be abelian

When I see things like that I worry. Commutative and abelian are synonyms.

CompuChip