Algebra/Chapter 25/Exercises

Exercises

Section 25.2

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

Section 25.3

25.2 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 $x^{-1}$.