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RD Sharma is considered as the best material for maths as it contains in detail explanation for questions and concepts. It is widely used by many CBSE schools in the country. Many teachers use this book as a reference for lectures and setting up question papers. This is why it is the best choice for students to prepare for their exams.

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**Also Read - **RD Sharma Solution for Class 9 to 12 Maths

- Chapter 6 - Adjoint & Inverse of Matrix Ex 6.1
- Chapter 6 - Adjoint & Inverse of Matrix Ex 6.2
- Chapter 6 - Adjoint & Inverse of Matrix Ex FBQ
- Chapter 6 - Adjoint & Inverse of Matrix Ex VSA

Adjoint and inverse of a matrix exercise multiple choice questions question

Given: A is an invertible matrix of order 3

Hints: A inverse is possible only when

∴ Option A is correct

Now option B,

We know that in of invertible matrix

∴ Option B is also correct

Now option D

(∴ A & B two invertible matrices of the same order)

Now, option C

B A = C A

⇒B=C

But it is given B ≠ C. Hence Option C is not true.

Adjoint and inverse of a matrix exercise multiple choice questions question 3

Given:

Hint: add the matrices A and B then find the inverse

Solution:

Now,

Hence,

We can clearly see that exists. So, option (c) is incorrect.

Now we will check the other options.

This shows option (b) is incorrect.

It is not skew symmetric matrix and for this we will Show

From the above calculation

Hence option (d) is correct.

Adjoint and inverse of a matrix exercise multiple choice questions question 4

Given:

Hint: find adjoint S by finding cofactors and transposing it.

Solution :

Adjoint and inverse of a matrix exercise multiple choice questions question 5

Given: A is a singular matrix

Hint: when matrix is singular

Solution:

We know that

Hence, matrix is singular then adjoint is also singular. So, option b is correct

Adjoint and inverse of a matrix exercise multiple choice questions question 6

Answer:

Given: A & B are non-singular matrix

Hint: A & B are singular matrices only when the is equal to Zero

Solution:

If A & B are non-singular matrices of order nxn

∴ AB is non-singular

Hence option (a) is correct.

Adjoint and inverse of a matrix exercise multiple choice questions question 7

Given:

Hint: Find , find adj A

Solution:

Hence, option c is correct.

Adjoint and inverse of a matrix exercise multiple choice questions question 8

Given:

Hint: calculate adjoint of A and put the value in it.

Solution:

Where n=3 because of 3×3 matrices

Hence, option (a) is correct.

Adjoint and inverse of a matrix exercise multiple choice questions question 9

Given: B is non-singular matrix and A is square matrix

Hint: Use the property B

Solution:

Hence, option (c) is correct.

Adjoint and inverse of a matrix exercise multiple choice question question 10

Give:

Hint: calculating determinant of A i.e; |A|

Solution:

We know that

Pre- multiplying by ‘A’

Hence option (c) is correct

Adjoint and inverse of a matrix exercise multiple choice question question 11

Given:

Hint: zero matrix is that whose every element is zero

Solution:

Hence, option (d) is correct

Adjoint and inverse of a matrix exercise multiple choice question question 12

Given: A satisfies the equation

Hint: since A satisfies the equation so put x = A

Solution :

Since A satisfies the equation ∴

A

since if then the above equation gives A = 0 and in that case A

Hence option (d) is correct.

Adjoint and inverse of a matrix exercise multiple choice question question 13

Given:

Hint: to find A

Solutions:

Post multiplying by A

Hence, option (a) is correct

Adjoint and inverse of a matrix exercise multiple choice question question 14

Given: A & B are square matrices and

Hint: to solve the question you must know the formula of

Solution:

Multiply both sides with A

Hence, option b is correct

Adjoint and inverse of a matrix exercise multiple choice question question15

Given:

Hint: you must know the multiplication concept of matrices

Solution:

Hence, option (c) is correct

Adjoint and inverse of a matrix exercise multiple choice question question 16

Answer:

Given: A, B & C are non-singular square matrices of same orders

Hint: to find the answer you must know the properties of inverse

Solution:

Hence, option (d) is correct

Adjoint and inverse of a matrix exercise multiple choice question question 17

Given: is a singular matrices

Hint: for any singular matrix, the value of the determinant is 0

Solution:

Hence, b is non-exist

∴ option (d) is correct

Adjoint and inverse of a matrix exercise multiple choice question question 18

Answer:

Given: d is the determinant of a square matrix A of order n

Hint: you must know the formula of

Solution:

Adjoint and inverse of a matrix exercise multiple choice question question 19

Given:

Hint: to find the answer, put the given value in the formula

Solution:

Hence, option (d) is correct

Adjoint and inverse of a matrix exercise multiple choice question question 20

Given:

Hint: use multiplication formula to find the answer

Solution:

Post – multiply both sides by A

Hence , option (c) is correct

Adjoint and inverse of a matrix exercise multiple choice question question 21

Given: A & B are invertible matrices

Hint: correct option is that whose right hand side is not equal to left hand side.

Solution :

We know that

Option (a) is correct

Option (b) is also correct

Hence, option (c) is answer

Adjoint and inverse of a matrix exercise multiple choice question question 22

Given: A is a square matrix such that

Hint: you must know about the concept of square matrix

Solution:

Multiply both sides by

Hence, option (b) is correct

Adjoint and inverse of a matrix exercise multiple choice question question 23

Given: and

X be a matrix such that A = BX

Hint: put A & B in equation and square to find matrix X.

Solution: – A= BX

Hence, option (a) is correct

Adjoint and inverse of a matrix exercise multiple choice question question 24

Given:

Hint: simply multiply the matrices

Hence, option (b) is correct

Adjoint and inverse of a matrix exercise multiple choice question question 26

Given:

Hint: identity matrix is that whose diagonal elements is 1 and rest and zero

Solution:

Now, value of a & b is not given so it is not solved further

Hence, option (d) is correct

Adjoint and inverse of a matrix exercise multiple choice question question 27

Hint: use simple matrix multiplication.

Solution :

Hence, option (b) is correct

Adjoint and inverse of a matrix exercise multiple choice question question 28

Given:

Hint: use simple calculation to get the result.

Hence, option (d) is correct

Adjoint and inverse of a matrix exercise multiple choice question question 29

Given – A is an invertible matrix

Hint – you must know about invertible matrix concept

Solution –

We know that

Hence, is option (b) is correct

Adjoint and inverse of a matrix exercise multiple choice question question 30

Given

Hint – find the value of A

Solution

Therefore, when n is odd and when n is even

Hence, option (a) is correct

Adjoint and inverse of a matrix exercise multiple choice question question 31

Given

Hint – Find the inverse of matrix A using the formula:

Solution-

Hence, option (a) is correct.

Adjoint and inverse of a matrix exercise multiple choice question question 32

Given – A & B are invertible matrices.

Hint – answers is that whose left have side is not equal to right hand side.

Hence option (d) is correct

Adjoint and inverse of a matrix exercise multiple choice question question 33

Given

Hint- find the value of |A|

Solution –

Hence, option (d) is correct

Adjoint and inverse of a matrix exercise multiple choice question question 34

Given – A is a square matrix &

Hint –Use the concept of square of identity matrix

Hence, option (a) is correct

Adjoint and inverse of a matrix exercise multiple choice question question 35

Given -

Hint – Find the determinant of A i.e,

Solution – since matrix is not invertible

**MCQs to get a good understanding of all the concepts in this chapter. **

Career360 has prepared RD Sharma Class 12th Chapter 6 MCQ specifically for students to save time and prepare for their exams. As exercise problems can be time consuming, MCQs are basically a distraction from those problems. In order to complete these quickly students can refer to this material.

As the board exams have 20 marks reserved for MCQs it is essential that students get each and everyone right. RD Sharma Class 12th Chapter 6 MCQ solutions is designed to help students prepare well for the MCQs. Solving all the MCQs is a tiring task and will use up a lot of time.

A majority of students spend a lot of time-solving MCQs and then panic when there’s no time left for main questions. RD Sharma Class 12th Chapter 6 MCQ material helps to get a clear understanding with the help of solutions and can help students divide the work to study systematically. If students stay in line with their class lectures and practice this material, there is nothing else they will need to score well in exams. As RD Sharma books are widely used in CBSE schools, it is possible that questions from this might appear in the exams.

RD Sharma books come up with a new version occasionally, it gets hard for students to keep track of the latest version materials. This means that as soon as the new version is released, the older materials become less helpful. RD Sharma Class 12 Chapter 6 MCQ by Career360 is updated to the latest version which means that students won’t have to worry about missing or different questions.

RD Sharma Class 12 Solutions Chapter 6 MCQ material is prepared by experts who have years of experience and insight on exam patterns. These solutions are meant to provide students with the best source of preparation and get them a unified material for all their chapters.

The best part about it is that it is free to download and available on Career360’s website. Thousands of students have already joined the team and started preparing for their exams using this material. If students didn’t know about this, they should definitely give it a try.

- Chapter 1 - Relations
- Chapter 2 - Functions
- Chapter 3 - Inverse Trigonometric Functions
- Chapter 4 - Algebra of Matrices
- Chapter 5 - Determinants
- Chapter 6 - Adjoint and Inverse of a Matrix
- Chapter 7 - Solution of Simultaneous Linear Equations
- Chapter 8 - Continuity
- Chapter 9 - Differentiability
- Chapter 10 - Differentiation
- Chapter 11 - Higher Order Derivatives
- Chapter 12 - Derivative as a Rate Measurer
- Chapter 13 - Differentials, Errors and Approximations
- Chapter 14 - Mean Value Theorems
- Chapter 15 - Tangents and Normals
- Chapter 16 - Increasing and Decreasing Functions
- Chapter 17 - Maxima and Minima
- Chapter 18 - Indefinite Integrals
- Chapter 19 - Definite Integrals
- Chapter 20 - Areas of Bounded Regions
- Chapter 21 - Differential Equations
- Chapter 22 - Algebra of Vectors
- Chapter 23 - Scalar Or Dot Product
- Chapter 24 - Vector or Cross Product
- Chapter 25 - Scalar Triple Product
- Chapter 26 - Direction Cosines and Direction Ratios
- Chapter 27 - Straight Line in Space
- Chapter 28 - The Plane
- Chapter 29 - Linear programming
- Chapter 30- Probability
- Chapter 31 - Mean and Variance of a Random Variable

1. Does this material contain all solutions?

Yes, Class 12 RD Sharma Chapter 6 MCQ Solution covers the entire syllabus and has all the solutions.

2. Where can I find solutions for the next exercise?

Students can find their solutions at Career360’s website.

3. Is RD Sharma better than NCERT

Yes, RD Sharma's maths books are more detailed than NCERT which gives them the advantage.

4. What is the inverse of a Matrix?

A Matrix, when multiplied by its inverse, should result in an identity Matrix. That is called the inverse value of a Matrix. For more info, check RD Sharma Class 12th Chapter 6 MCQ.

5. Can I save time studying this material?

Yes, indeed, as RD Sharma Class 12 Solutions Adjoint and Inverse of Matrix MCQ contains all the solutions that students can refer to and save a lot of time.

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