From our intuitive grasp of the notion of isomorphic groups, it should be clear that if ∅ : G ➔ G' is a group isomorphism, then ∅(e) is the identity e' of G'. Recall that Theorem 3.14 gave a proof of this for isomorphic binary structures ( S, *) and ( S', *'). Of course, this covers the case of groups. 

It should also be intuitively clear that if a and a' are inverse pairs in G, then ∅(a) and ∅(a') are inverse pairs in G', that is, that ∅(a)' = ∅(a'). Give a careful proof of this for a skeptic who can't see the forest for all the trees.