Algebra/Chapter 27/Exercises

Exercises

Section 27.2

27.1 Assume that * is a binary operation on the set S. Prove the following statements.

Section 27.3

27.2 Let $G$ be a group. Prove that the identity element $e\in G$ is unique. Also prove that every element $x\in G$ has a unique inverse, indicated by $x^{-1}$.