   Chapter 1.4, Problem 15E

Chapter
Section
Textbook Problem
1 views

# Let ∗ be a binary operation on the non empty set A . Prove that if A contains an identity element with respect to ∗ , the identity element is unique.

To determine

To prove: If A contains an identity element with respect to , the identity element is unique, where be a binary operation on the non empty set A.

Explanation

Given Information:

be a binary operation on the non empty set A.

Formula Used:

If e is the identity element of A and aA then, ea=ae=a.

Explanation:

Let e and f both are the identity elements of A. Then for any xA, ex=xe=x and fx=xf=x.

Now, since e is an identity and fA, then ef=f………

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Find more solutions based on key concepts 