For binary operation

* : A × A → A

with identity element e

 

For element a in A,

there is an element b in A

such that

  a * b = e = b * a

Then, b is called inverse of a

 

Addition

+ : R × R R

 

For element a in A,

there is an element b in A

such that

  a * b = e = b * a

Then, b is called inverse of a

 

Here, e = 0 for addition

So, a * b = e = b * a

      a + b = 0 = b + a

⇒ b = –a

 

Since

  a + (– a) = 0 = (– a) + a,

So, –a is the inverse of a for addition.

 


Multiplication

× : R × R R

 

An element a in R is invertible if,

there is an element b in R such that ,

a * b = e = b * a

Here, b is the inverse of a

 

Here, e = 1 for multiplication

So, a * b = e = b * a

      a × b = 1 = b × a

⇒ b = 1/a

 

Since

  a × 1/a = 1 = 1/a × a

So,  1/a is the inverse of a for multiplication.

  1. Chapter 1 Class 12 Relation and Functions
  2. Concept wise
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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 7 years. He provides courses for Mathematics and Science from Class 6 to 12. You can learn personally from here https://www.teachoo.com/premium/maths-and-science-classes/.
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