I also got stuck on this one, while I was studying for my final, any help appreciated!

Let f:A->B and g:B->A. Let IA and IB be the identity functions on the sets A and B, respectively. Prove each of the following:

a) If g of f = IA, then f is an injection.

b) If f of g = IB, then f is a surjection.

c) If g of f = IA and f of g = IB, then f and g are bijections and g = f^-1

**f^-1 means f inverse.