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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,
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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.
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Hi Madhuri,
For CBSE Class 12 Maths preparation, especially if your basics are weak, please refer to the link given below:
https://school.careers360.com/boards/cbse/cbse-class-12-maths-preparation-tips
Hi Jatin!
Given below is the link to access CBSE Class 12 English Previous Year Questions:
https://school.careers360.com/download/ebooks/cbse-class-12-english-previous-year-question-papers
For subjectwise previous year question papers, you might find this link useful:
https://school.careers360.com/boards/cbse/cbse-previous-year-question-papers-class-12
Dear Student,
If you have 6 subjects with Hindi as an additional subject and you have failed in one compartment subject, your additional subject which is Hindi can be considered pass in the board examination.
Hi,
The CBSE Class 10 Computer Applications exam (Set-1) was conducted on 27 February 2026 from 10:30 AM to 12:30 PM as part of the CBSE board exams. The paper included MCQs, very short answer questions, short answers, long answers, and case-study questions based on topics like HTML, networking, internet
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