2.7 Prove that if theta:S-T, then theta(composition)identity=theta and identity(composition)theta=theta
2.20 Prove that the inverse of an invertible mapping is invertible
2.7. Denote the identity mapping of S by iS and the identity mapping in T by iT (are not these two in the statement given in the text?). Now we have: q° iS(x)=q(iS(x)) by definition of composition; further q(iS(x))=q(x) because iS(x) = x; similarly iT° q(x)) = q(x). So the mappings do the same thing to each x, and so they are equal.
2.20. It follows from the definition of inverse mapping that the inverse of the inverse of a is a. So, the inverse of a is invertible.