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: If a matrix A = [ 1 2 3] then order of matrix A ?
A:
The order of matrix A is 1x3.
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: 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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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 medical or engineering) may give slight preference to GSEB students for state-level counselling, not for all courses.
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The Central Board of Secondary Education (CBSE) releases the previous year's question papers for Class 12.
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On our official website, you can download the class 12th practice question paper for all the commerce subjects (accountancy, economics, business studies and English) in PDF format with solutions as well.
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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.
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