# NCERT Solutions for Exercise 3.4 Class 12 Maths Chapter 3 - Matrices

In the NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.4, you will get questions related to elementary operation on the matrix. Elementary operations or transformations are a set of operations that are allowed to perform on the matrix to get transformed matrix. These transformations are useful in the finding inverse of a matrix if exists. If the inverse of a matrix exists then it is called an invertible matrix. There are some questions in **exercise 3.4** Class 12 Maths where you need to find the inverse of a matrix using elementary operation. NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.4 is very important as generally one question is directly asked from this exercise in the CBSE board final exam. Class 12 maths ch 3 ex 3.4 required more practice and the chances of silly mistakes are more here, so you must practice all the questions in order to get them correct in the board exam. You can check NCERT solutions here.

**Also, see**

- Matrices Exercise 3.1
- Matrices Exercise 3.2
- Matrices Exercise 3.3
- Matrices Miscellaneous Exercise

**Matrices Exercise: 3.4**

**Question 1 **Using elementary transformations, find the inverse of each of the matrices, if it exists

in Exercises 1 to 17.

** **

**Answer:**

Use the elementary transformation we can find the inverse as follows

**Question 2 **Using elementary transformations, find the inverse of each of the matrices, if it exists

in Exercises 1 to 17.

** **

**Answer:**

Thus we have obtained the inverse of the given matrix through elementary transformation

**Question 3 **Using elementary transformations, find the inverse of each of the matrices, if it exists

in Exercises 1 to 17.

** **

**Answer:**

Using elementary transformations

.

**Question 4 **Using elementary transformations, find the inverse of each of the matrices, if it exists

in Exercises 1 to 17.

**Answer:**

**Question 5 **Using elementary transformations, find the inverse of each of the matrices, if it exists

in Exercises 1 to 17.

**Answer:**

.

Thus the inverse of matrix A is obtained.

**Question 6 **Using elementary transformations, find the inverse of each of the matrices, if it exists

in Exercises 1 to 17.

**Answer:**

Use the elementary transformation

** **

.

**Question 7 **Using elementary transformations, find the inverse of each of the matrices, if it exists

in Exercises 1 to 17.

** **

**Answer:**

.

Thus the inverse of matrix A is obtained using elementary transformation.

**Question 8 **Using elementary transformations, find the inverse of each of the matrices, if it exists

in Exercises 1 to 17.

**Answer:**

Thus using elementary transformation inverse of A is obtained as

.

**Question 9 **Using elementary transformations, find the inverse of each of the matrices, if it exists

in Exercises 1 to 17.

**Answer:**

Thus using elementary transformation the inverse of A is obtained as

.

**Question 10 **Using elementary transformations, find the inverse of each of the matrices, if it exists

in Exercises 1 to 17.

**Answer:**

.

Thus the inverse of A is obtained using elementary transformation.

**Question 11 **Using elementary transformations, find the inverse of each of the matrices, if it exists

in Exercises 1 to 17.

**Answer:**

thus the inverse of matrix A is

.

**Question 12 **Using elementary transformations, find the inverse of each of the matrices, if it exists

in Exercises 1 to 17.

** **

**Answer:**

Hence, we can see all the zeros in the second row of the matrix in L.H.S so does not exist.

**Question 13 **Using elementary transformations, find the inverse of each of the matrices, if it exists

in Exercises 1 to 17.

**Answer:**

** **

so the inverse of matrix A is

.

**Question 14 **Using elementary transformations, find the inverse of each of the matrices, if it exists

in Exercises 1 to 17.

**Answer:**

Hence, we can see all upper values of matirix are zeros in L.H.S so does not exists.

**Question 15 **Using elementary transformations, find the inverse of each of the matrices, if it exists

in Exercises 1 to 17.

**Answer:**

Thos the Inverse of A is

..

**Question 16 **Using elementary transformations, find the inverse of each of the matrices, if it exists

in Exercises 1 to 17.

**Answer:**

and

and

and

Thus the inverse of three by three matrix A is

..

**Question 17 **Using elementary transformations, find the inverse of each of the matrices, if it exists

in Exercises 1 to 17.

**Answer:**

and

Thus the inverse of A is obtained as

..

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

(A)

(B)

(C)

(D)

**Answer:**

We know that if A is a square matrix of order n and there is another matrix B of same order n, such that , then B is inverse of matrix A.

In this case, it is clear that A is inverse of B.

Hence, **m**atrices A and B will be inverse of each other only if .

Option D is correct.

**More about NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.4:- **

In Class 12th Maths chapter 3 exercise 3.4, there are 18 questions out of which 17 questions are related to finding the inverse of a matrix using elementary operations if exists. One multiple choice type question is related to the condition of an invertible matrix. There are 3 solved examples and some theorems given before the NCERT text book exercise 3.4 Class 12 Maths. Examples related to finding the inverse of a matrix are also given in Class 12 Maths ch 3 ex 3.4. Theorems given in the NCERT syllabus are important to get conceptual clarity.

**Also Read| ****Matrices Class 12 Maths Chapter Notes**

**Benefits of NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.4:-**

- Class 12 Maths chapter 3 exercise 3.4 solutions are helpful for the students in the board exams as well as in competitive exams.
- NCERT problems are solved by experts who have good knowledge and experience so you can rely upon them.
- NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.4 are beneficial for the students who are not able to solve some difficult problems.
- Students are advised to solve all the NCERT problems including examples as most of the questions in the board exams are directly asked from the NCERT textbook.

**Also see-**

NCERT solutions for class 12 maths chapter 3

NCERT exemplar solutions class 12 maths chapter 3

**NCERT solutions of class 12 subject wise**

NCERT solutions for class 12 Maths

NCERT solutions for class 12 Physics

NCERT solutions for class 12 Chemistry

NCERT solutions for class 12 Biology

**Subject wise NCERT Exampler solutions**

5 Psychometric Tests Every Student Must Take 9 min read Mar 05, 2022 Read More Rote Learning Vs Smart Learning - Which One Is More Effective? 7 min read Mar 05, 2022 Read More

NCERT Exemplar Solutions for Class 12th Maths

NCERT Exemplar Solutions for Class 12th Physics

NCERT Exemplar Solutions for Class 12th Chemistry

NCERT Exemplar Solutions for Class 12th Biology

**Happy learning!!!**