I want to know the answer to the following question:
How can showing the second equality yields the first prove the concept of isomorphic groups?
All the background I'm provided with is that "For example, proving that g • g = 1G for some element g of G is equivalent to proving that a(g) ∗ a(g) = 1H, because applying a to the first equality yields the second, and applying b to the second gives back the first.". Is that enough to answer the question?