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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.
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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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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
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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.
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Hello Pawan,
CBSE Class 10 Mathematics 2026 and previous year question paper:
https://school.careers360.com/boards/cbse/cbse-class-10-question-paper-2026
CBSE Class 12 Mathematics 2026 and previous year question paper:
https://school.careers360.com/boards/cbse/cbse-previous-year-question-papers-class-12-maths
Hello Dharani,
Check the link below to download NCERT Class 12 previous year question papers in PDF format for all subjects.
https://school.careers360.com/boards/cbse/cbse-previous-year-question-papers-class-12
Hello Vipin,
Check the link below to download CBSE Class 12 question papers in PDF format for all subjects, including Mathematics.
https://school.careers360.com/boards/cbse/cbse-previous-year-question-papers-class-12
Hello Shubham,
NCERT Class 12 Chemistry chapter-wise notes and solutions are available at the link given below. Keep checking for updated uploads when NCERT PYQs (Previous Year Questions) are published.
https://school.careers360.com/ncert/ncert-solutions-class-12-chemistry
Hi!
Given below is the link to access CBSE Class 12 Sociology Question Paper 2026 with Answer Key:
https://school.careers360.com/boards/cbse/cbse-class-12-sociology-answer-key-2026
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