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

JEE Mains & Advanced

NCERT solutions for class 12 maths chapter 3 exercise 3.4 Matrices explains invertible matrices. In this exercise, you will learn some important theorems related to invertible matrices. Ex 3.4 class 12 maths chapter 3 solutions have included examples, and sample questions that deliver basic understanding of the topic. Our subject experts have develop these solutions, to promote error free learning.

Class 12 maths chapter 3 exercise 3.4 NCERT solutions are also available in PDF format at eSaral website. You must download these free PDFs of NCERT solutions to practice questions that will lead to achieving a high score in exams. To download the PDF, you can check the link mentioned below.

## Topics Covered in Exercise 3.4 Class 12 Mathematics Questions

Ex 3.4 class 12 maths chapter 3 goes in the detail of invertible matrices. You will study the definition of invertible matrices, its applications and theorems related to invertible matrices.

 1 Invertible Matrices
1. Invertible Matrices - If A is a square matrix of order m, and if there exists another square matrix B of the same order m, such that AB = BA = I, then B is called the inverse matrix of A and it is denoted by A– 1. In that case A is said to be invertible.

Theorem 3:  (Uniqueness of inverse) Inverse of a square matrix, if it exists, is unique.

Theorem 4: If A and B are invertible matrices of the same order, then (AB)–1 = B–1 A–1 .

## Tips for Solving Exercise 3.4 Class 12 Chapter 3 Matrices

Ex 3.4 class 12 maths ch 3 NCERT solutions have included questions based on invertible matrices. To solve these questions, you must follow the tips given by subject experts of eSaral.

1. You should go through the definitions, theorems and solved examples to ensure complete preparation for board exams.

2. NCERT solutions class 12 maths chapter 3 ex 3.4 is very prominent to provide a comprehensive knowledge of invertible matrices which you must revise to score good marks in exams.

3. You should follow the step by step method provided by expert teachers of eSaral to solve each question with ease.

## Importance of Solving Ex 3.4 Class 12 Maths Chapter 3 Matrices

You can find here numerous benefits of solving ex 3.4 class 12 maths chapter 3 matrices. Some of them are mentioned below.

1. Solving questions in NCERT solutions class 12 maths chapter 3 ex 3.4 will provide you simple and straightforward answers to all questions.

2. All important terms, definitions and theorems of invertible matrices are explained by subject experts of eSaral to make sure each question is solved without any doubt.

3. NCERT solution PDFs are available on eSaral website which you can download free and practice all questions at your own pace.

4. Practicing questions and revising topics will increase your self-confidence and improve your problem solving skills in examinations.

#### Frequently Asked Questions

Question 1. What are invertible matrices?

Answer 1.  If A is a square matrix of order m, and if there exists another square matrix B of the same order m, such that AB = BA = I, then B is called the inverse matrix of A and it is denoted by A– 1. In that case A is said to be invertible.

Question 2. What is the uniqueness of inverse?

Answer 2.  (Uniqueness of inverse) Inverse of a square matrix, if it exists, is unique.

If A = [aij] be a square matrix of order m. If possible, let B and C be two inverses of A. We shall show that B = C.

Since B is the inverse of A

Then AB = BA = I

Since C is also the inverse of A

Similarly AC = CA = I

Thus it proves B = BI = B (AC) = (BA) C = IC = C

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