Assignment:
Q1. Let (A, *) be an algebraic structure, and suppose that A is associative, has an identity, e, and that a ∈ A has an inverse. Show that if ax = ay, then x = y.
Q2. Let G be a finite group with identity e, and let a ∈G. Show that there is an n ∈ N with an = e (Hint: Consider the set {e, a, a2 , ..., am }, where m is the number of elements of G and use cancellation.)
Provide complete and step by step solution for the question and show calculations and use formulas.