NCERT Solutions for Exercise 3.4 Class 12 Maths Chapter 3 - 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 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
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 $\mathrm{AB}=\mathrm{BA}=\mathrm{I}$, then B is called the inverse matrix of A and it is denoted by $\mathrm{A}^{-1}$. 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 $(\mathrm{AB})^{-1}=\mathrm{B}^{-1} \mathrm{~A}^{-1}$.
Also, read,
JEE Main Highest Scoring Chapters & Topics
Just Study 40% Syllabus and Score upto 100%
Download EBookNCERT 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.
CBSE Class 12th Syllabus: Subjects & Chapters
Select your preferred subject to view the chapters
Subject-wise NCERT Exemplar solutions
Students can explore these NCERT exemplar links for additional practice.
Frequently Asked Questions (FAQs)
Q: What of the definition of elements in a matrix ?
A:
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.
Q: If a matrix A = [ 1 2 3] then order of matrix A ?
A:
The order of matrix A is 1x3.
Q: write some types of matrix ?
A:
A square matrix, zero or null matrix, scalar matrix, diagonal matrix, row matrix, and column matrix are some types of matrices.
Q: Two matrices A and B are inverse of each other only if ?
A:
If AB = BA = I, then A and B are inverses of each other.
Q: What is the condition for addition of two matrices ?
A:
The order of matrices has to be the same in order to add them.
Q: Can we add matrix A of order 2x3 and matrix B of 3x2 ?
A:
No, as the order of both the matrices are not the same.
Q: Can we multiply matrix A of order 2x3 and matrix B of 3x2 ?
A:
Yes, matrices A and B can be multiplied
Q: What is order of the matrix we get when we multiply matrix A of order 2x3 and matrix B of 3x2 ?
A:
The order of the solution matrix will be 2x2.
Articles
Related Stories
|
Upcoming School Exams
Certifications By Top Providers
Explore Top Universities Across Globe
Questions related to CBSE Class 12th
On Question asked by student community
Have a question related to CBSE Class 12th ?
Failing in pre-board or selection tests does NOT automatically stop you from sitting in the CBSE Class 12 board exams. Pre-boards are conducted by schools only to check preparation and push students to improve; CBSE itself does not consider pre-board marks. What actually matters is whether your school issues your
The CBSE Sahodaya Class 12 Pre-Board Chemistry Question Paper for the 2025-2026 session is available for download on the provided page, along with its corresponding answer key.
The Sahodaya Pre-Board exams, conducted in two rounds (Round 1 typically in December 2025 and Round 2 in January 2026), are modeled precisely
Hello,
You can get the Class 11 English Syllabus 2025-26 from the Careers360 website. This resource also provides details about exam dates, previous year papers, exam paper analysis, exam patterns, preparation tips and many more. you search in this site or you can ask question we will provide you the
Hello,
No, it’s not true that GSEB (Gujarat Board) students get first preference in college admissions.
Your daughter can continue with CBSE, as all recognized boards CBSE, ICSE, and State Boards (like GSEB) which are equally accepted for college admissions across India.
However, state quota seats in Gujarat colleges (like
Hello,
The Central Board of Secondary Education (CBSE) releases the previous year's question papers for Class 12.
You can download these CBSE Class 12 previous year question papers from this link : CBSE Class 12 previous year question papers (http://CBSE%20Class%2012%20previous%20year%20question%20papers)
Hope it helps !
Popular CBSE Class 12th Questions
A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is
| Option 1)
|
Option 2)
|
| Option 3)
|
Option 4)
|
An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range
| Option 1)
|
Option 2)
|
| Option 3)
|
Option 4)
|
A particle is projected at 600 to the horizontal with a kinetic energy . The kinetic energy at the highest point
| Option 1)
|
Option 2)
|
| Option 3)
|
Option 4)
|
In the reaction,
| Option 1)
|
Option 2)
|
| Option 3)
|
Option 4)
|
How many moles of magnesium phosphate, will contain 0.25 mole of oxygen atoms?
| Option 1)
0.02 |
Option 2)
3.125 × 10-2 |
| Option 3)
1.25 × 10-2 |
Option 4)
2.5 × 10-2 |
Colleges After 12th
Applications for Admissions are open.
As per latest syllabus. Physics formulas, equations, & laws of class 11 & 12th chapters
JEE Main Important Chemistry formulas
Get nowAs per latest syllabus. Chemistry formulas, equations, & laws of class 11 & 12th chapters
JEE Main high scoring chapters and topics
Get nowAs per latest 2024 syllabus. Study 40% syllabus and score upto 100% marks in JEE
JEE Main Important Mathematics Formulas
Get nowAs per latest syllabus. Maths formulas, equations, & theorems of class 11 & 12th chapters
CBSE Class 12th Notifications
Never miss CBSE Class 12th update
Get timely CBSE Class 12th updates directly to your inbox. Stay informed!