NCERT Solutions for Exercise 3.4 Class 12 Maths Chapter 3 - Matrices
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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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Hello,
Since you have passed 10th and 12th from Delhi and your residency is Delhi, but your domicile is UP, here’s how NEET counselling works:
1. Counselling Eligibility: For UP NEET counselling, your UP domicile makes you eligible, regardless of where your schooling was. You can participate in UP state counselling according to your NEET rank.
2. Delhi Counselling: For Delhi state quota, usually 10th/12th + residency matters. Since your school and residency are in Delhi, you might also be eligible for Delhi state quota, but it depends on specific state rules.
So, having a Delhi Aadhaar will not automatically reject you in UP counselling as long as you have a UP domicile certificate.
Hope you understand.
Hello,
You can access Free CBSE Mock tests from Careers360 app or website. You can get the mock test from this link : CBSE Class 12th Free Mock Tests
Hope it helps !
Yes, it is possible for a student who has done their 12th grade already to take upto 4 exams of their requirement. This is possible through the NIOS, NATIONAL INSTITUTE OF OPEN SCHOOLING. Get more info about the exam and the board through the following link.
For CBSE the PREVIOUS YEARS PAPERS can be accessed through the following link for the Concerned subjec by careers360.
Consequently Careers360 does also have a chapter wise scheme of PYQs, you can access the STUDY MATERIAL (PYQs.) from the following link -
https://school.careers360.com/boards/cbse/cbse-question-bank
Thankyou.
Hello,
Sorry, but JoSAA does not accept marks from two different boards for the same qualification during counselling. However, you can use your NIOS marks to meet the JEE Main/Advanced eligibility criteria if they are better than your CBSE marks. You can use your NIOS marks for the eligibility check, but when presenting your documents, you may be required to present both marksheets and the one with the higher marks for each subject will be considered.
I hope it will clear your query!!
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