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

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

Updated on Apr 22, 2025 11:01 PM IST | #CBSE Class 12th

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 we denote B as the inverse matrix of A, A⁻¹. Here, we refer to matrix A as invertible. These solutions for Class 12, Chapter 3, Exercise 3.4 of NCERT have been developed by subject matter experts at Careers360 to give more clarity of concepts and a proper approach to attempt the questions. These NCERT solutions for Class 12 Mathematics, Chapter 3, Exercise 3.4 hold significant importance because every year there is a question from this exercise in JEE and board examinations.

Class 12 Maths Chapter 3 Exercise 3.4 Solutions: Download PDF

Download PDF

Matrices Exercise: 3.4

Question:1 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

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 AB=BA=I, then B is inverse of matrix A.

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

Hence, matrices A and B will be inverse of each other only if AB=BA=I.

Option D is correct.


Also Read,

Topics covered in Chapter 3: Matrices: Exercise 3.4

  • Introduction
  • Invertible matrix: 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: The 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.
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NCERT solutions for class 12 maths chapter 3

NCERT exemplar solutions class 12 maths chapter 3

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NCERT Solutions Subject Wise

These links pertain to solutions for NCERT textbooks across various subjects. Students are encouraged to review and analyse these meticulously structured solutions to enhance their comprehension.

Subject-wise NCERT Exemplar solutions

Students can explore these NCERT exemplar links for additional practice.

Frequently Asked Questions (FAQs)

1. If a matrix A = [ 1 2 3] then order of matrix A ?

The order of matrix A is 1x3.

2. What of the definition of elements in a matrix ?

The numbers or functions that exist in the rows and columns of a particular matrix are called elements of the matrix. Definitions, examples and questions are given in the NCERT book. For more practice problems NCERT exemplar for class 12 Maths can be used. Practice class 12 ex 3.4 to command the concepts.

3. write some types of matrix ?

A square matrix, zero or null matrix, scalar matrix, diagonal matrix,  row matrix, and column matrix are some types of matrices.

4. Two matrices A and B are inverse of each other only if ?

If AB = BA = I, then A and B are inverses of each other.

5. What is the condition for addition of two matrices ?

The order of matrices has to be the same in order to add them.

6. Can we add matrix A of order 2x3 and matrix B of 3x2 ?

No, as the order of both the matrices are not the same.

7. Can we multiply matrix A of order 2x3 and matrix B of 3x2 ?

Yes, matrices A and B can be multiplied

8. What is order of the matrix we get when we multiply matrix A of order 2x3 and matrix B of 3x2 ?

The order of the solution matrix will be 2x2.

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Questions related to CBSE Class 12th

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Can I change my board from CBSE to CHSE Odisha in Class 12th?

Changing from the CBSE board to the Odisha CHSE in Class 12 is generally difficult and often not ideal due to differences in syllabi and examination structures. Most boards, including Odisha CHSE , do not recommend switching in the final year of schooling. It is crucial to consult both CBSE and Odisha CHSE authorities for specific policies, but making such a change earlier is advisable to prevent academic complications.

Read Complete Answer
Manasvini Gupta 30 January,2025
quartely question paper for mathematics cbse

Hello there! Thanks for reaching out to us at Careers360.

Ah, you're looking for CBSE quarterly question papers for mathematics, right? Those can be super helpful for exam prep.

Unfortunately, CBSE doesn't officially release quarterly papers - they mainly put out sample papers and previous years' board exam papers. But don't worry, there are still some good options to help you practice!

Have you checked out the CBSE sample papers on their official website? Those are usually pretty close to the actual exam format. You could also look into previous years' board exam papers - they're great for getting a feel for the types of questions that might come up.

If you're after more practice material, some textbook publishers release their own mock papers which can be useful too.

Let me know if you need any other tips for your math prep. Good luck with your studies!

Read Complete Answer
Jefferson 25 September,2024
i have taken admission in clg after my campartment exam in chemistry along with the neet 2025 preperation but unfortunately i again got campartment after doing all this preparation i got 15 marks only now I can't able to think what should I do next.

It's understandable to feel disheartened after facing a compartment exam, especially when you've invested significant effort. However, it's important to remember that setbacks are a part of life, and they can be opportunities for growth.

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Remember: This is a temporary setback. With the right approach and perseverance, you can overcome this challenge and achieve your goals.

I hope this information helps you.







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Kanishka kaushikii 17 September,2024
i scored 84 percent in cbse 2 years ago.Am i eligible for medhavi scholarship if give 12th again after 2 drop years and will got 75+ in mpboard

Hi,

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Yuvan 30 August,2024
i upload 12th board result screenshot in ncweb form from the cbse site so it is valid

hello mahima,

If you have uploaded screenshot of your 12th board result taken from CBSE official website,there won,t be a problem with that.If the screenshot that you have uploaded is clear and legible. It should display your name, roll number, marks obtained, and any other relevant details in a readable forma.ALSO, the screenshot clearly show it is from the official CBSE results portal.

hope this helps.

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Ashvadha 12 July,2024
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