Check sibling questions

For binary operation

* : A × A → A

 

e is called identity of * if

  a * e  = e * a = a

Here e is called identity element of binary operation.

 


Addition

+ : R × R R

 

e is called identity of * if

  a * e  = e * a = a

i.e.

  a + e = e + a = a

 

This is only possible if e = 0

 

Since a + 0 = 0 + a = a ∀ a ∈ R

0 is the identity element for addition on R

 


Multiplication

e is the identity of * if

a * e  = e * a = a

i.e. a × e = e × a = a

This is possible if e = 1

 

Since a × 1 = 1 × a = a ∀ a ∈ R

1 is the identity element for multiplication on R

 


Subtraction

e is the identity of * if

a * e  = e * a = a

i.e. a – e = e – a = a

There is no possible value of e where a – e = e – a

 

So, subtraction has no identity element in R

 


Division

e is the identity of * if

a * e  = e * a = a

i.e. a/e = e/a = a

There is no possible value of e where a/e = e/a = a

 

So, division has no identity element in R *

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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.