Exercise 3.4

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NCERT Solutions class 12 Maths Matrices 

Using elementary transformation, find the inverse of each of the matrices, if it exists in Exercises 1 to 6.

1. 

Ans. Let A =

Since A = IA     

   =

2.    

Ans. Let A =

Since A = IA     

   =

3.  

Ans. Let A =

Since A = IA     

   =

4.      

Ans. Let A =

Since A = IA     

   =

5.    

Ans. Let A =

Since A = IA     

   =

6.  

Ans. Let A =

Since A = IA     

   =

NCERT Solutions class 12 Maths Exercise 3.4

Using elementary transformation, find the inverse of each of the matrices, if it exists in Exercises 7 to 14.

7.    

Ans. Let A =

Since A = IA     

   =

8.   

Ans. Let A =

Since A = IA     

   =

9.   

Ans. Let A =

Since A = IA     

   =

10.  

Ans. Let A =

Since A = IA     

   =

11.   

Ans. Let A =

Since A = IA     

   =

12.   

Ans. Let A =

Since A = IA     

Here, all entries in second row of left side are zero.

   does not exist.

13.

Ans. Let A =

Since A = IA     

   =

14.  

Ans. Let A =

Since A = IA     

Here, all entries in second row of left side are zero.

   does not exist.

NCERT Solutions class 12 Maths Exercise 3.4

Using elementary transformation, find the inverse of each of the matrices, if it exists in Exercises 7 to 14.

15.     

Ans. Let A = , We know that A = IA,    

16.    

Ans. Let A = , Since, A = IA     

   =

17.  

Ans. Let A = , Since, A = IA     

   =

NCERT Solutions class 12 Maths Exercise 3.4

18.  Matrices A and B will be inverse of each other only if:

(A) AB = BA 

(B) AB = BA = 0

(C) AB = 0, BA = I

(D) AB = BA = I

Ans. By definition of inverse of square matrix,

Option (A) is correct.