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## Homework Statement

## Homework Equations

## 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?

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