Question 25 - Examples - Chapter 1 Class 12 Relation and Functions

Last updated at August 11, 2026 by

Example 49 - Show number of binary operations on {1, 2} - Binary operations: Inverse

Example 49 - Chapter 1 Class 12 Relation and Functions - Part 2

Take a fresh quiz. Then take another.
Every attempt is a new AI-adaptive Teachoo quiz with 3 questions, selected from your answers, mistakes, and progress.
Remove Ads
Teachoo · Class 12 Explore Class 12

Transcript

Question 25 Show that the number of binary operations on {1, 2} having 1 as identity and having 2 as the inverse of 2 is exactly one. Given that 1 is identity e is the identity of * if a * e = e * a = a So, a * 1 = 1 * a = a Put a = 1 1 * 1 = 1 Put a = 2 1 * 2 = 2 * 1 = 1 Also, Given that 2 is inverse of 2 b is the inverse of a if a * b = b * a = e Here, e = 1 & a = 2, b = 2 So, 2 * 2 = 2 * 2 = 1 Hence, there is only 1 binary operation which satisfies the given conditions

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh is an IIT Kanpur graduate and has been teaching for 16+ years. At Teachoo, he breaks down Maths, Science and Computer Science into simple steps so students understand concepts deeply and score with confidence.

Many students prefer Teachoo Black for a smooth, ad-free learning experience.