1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution For the first question, since [f(a)][g(a)] is in C, can I just say that since C is a ring, it is an abelian group, then the four axioms are proven? Then just show closure? Probably not I'm guessing. Associativity of multiplying functions seems so fundamental to me that I really don't know what to do... For the second question, shall I start by using composition of functions and then the properties of composition of a function and its inverse, and then go on about the identity function?