Assignment:
Let G be a nonempty set closed under an associative product, which in addition satisfies:
(a) There exists an e in G such that e.a = a for all a in G.
(b) Given a in G, there exists an element y(a) in G such that y(a).a = e.
Then G is a group under this product.
Provide complete and step by step solution for the question and show calculations and use formulas.