Assignment:
Q1. Prove that if G is a finite group and a is an element of G then for some positive m , a^m is equal to the identity of G. (Use the Pigeon hole principle)
Q2. Prove that if G is a finite group, H subset of G that is closed with respect to the operation of G, Then every element of H has its inverse in H.
Provide complete and step by step solution for the question and show calculations and use formulas.