Check sibling questions

For binary operation

* : A × A → A

If (a, b) = (b, a)

Then it is commutative binary operation

 

Let's check some examples


Addition

+ : R × R R

Since a + b = b + a

Hence, + is a commutative binary operation

 


Multiplication

× : R × R R

Since a × b = b × a

Hence, × is a commutative binary operation

 


Subtraction

: R × R R

 

We have to check if

  a – b = b – a

 

Let a = 2 , b = 5

a – b = 2 – 5 = –3

b – a = 5 – 2 = 3

 

Since a – b ≠ b – a

Hence, – is not a commutative binary operation

 


Division

÷  : R * × R * R *

 

Here R* is all real numbers except 0

We have to check if

  a ÷ b = b ÷ a

 

Let a = 2 , b = 5

a ÷ b = a/b = 2/5

b ÷ a = b/a = 5/2

 

Since a ÷ b ≠ b ÷ a

Hence, ÷ is not a commutative binary operation

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.