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# NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.2 Matrices - PDF Download

NCERT solutions for class 12 maths chapter 3 exercise 3.2 Matrices involve problems based on arithmetic operations on matrices. Mathematical operations on matrices are primarily divided into three categories. They can be multiplied, subtracted, or added according to certain rules of using matrix algebra. Each element of a matrix can be performed to an individual element-wise arithmetic operation. This topic requires extensive practice and revision because it is very relevant to real-world situations.

Ex 3.2 class 12 maths chapter 3 solutions comprises a total of 22 questions related to these topics. eSaral’s subject experts have provided NCERT solutions in detailed manner in order to clarify all your doubts to solve questions of ex 3.2 class 12 maths ch 3. You can also download the free PDF of these solutions from the website of eSaral to prepare for exams. NCERT solution PDFs available here have all the solutions of exercise questions that will help you in practicing this chapter for the board exam. Download the PDF from the link mentioned below.

## Topics Covered in Exercise 3.2 Class 12 Mathematics Questions

Class 12 maths chapter 3 exercise 3.2 NCERT solutions is all about arithmetic operations on matrices such as addition, multiplication and you will also learn the properties of matrix addition, properties of scalar multiplication of a matrix, multiplication of matrices etc.

 1 Operations on Matrices Addition of matrices Multiplication of a matrix by a scalar Properties of matrix addition Properties of scalar multiplication of a matrix Multiplication of matrices Properties of multiplication of matrices
1. Operations on Matrices - We will cover a few matrix operations in this part, including addition of matrices, multiplication of matrix by a scalar, difference and multiplication of matrices.

(I) Two matrices can only be added if their orders are the same.

(II) The sum of two matrices is a matrix obtained by adding the corresponding elements of the given matrices.

• Multiplication of a matrix by a scalar

When a matrix is multiplied by a scalar, then every element of the matrix is multiplied by the scalar quantity and a new matrix is produced.

1. Negative of a matrix - When a matrix is multiplied by −1, the resultant matrix is negative.

2. Difference of matrices - It is only possible to subtract two matrices if their orders are the same. You can perform a subtraction by deducting the corresponding entries of two matrices.

• Properties of matrix addition - The following properties are satisfied by the addition of matrices:

(i) Commutative Law - Addition to a matrix is commutative. i.e.  A+B=B+A

(ii) Associative Law - Addition to a matrix is associative. i.e. (A+B)+C=A+(B+C)

(iii) Existence of additive identity - Since a matrix remains unchanged when a zero matrix is added, zero matrix O is the additive identity of a matrix. i.e. A + O = O + A = A.

(iv) The existence of additive inverse - When a matrix is added to another matrix, it becomes its additive inverse. i.e. A + (– A) = (– A) + A= O.

•  Properties of scalar multiplication of a matrix - If A = [aij] and B = [bij] be two matrices of the same order, say m × n, and k and l are scalars, then

(i) k(A +B) = k A + kB, (ii) (k + l)A = k A + l A

(ii) k (A + B) = k ([aij] + [bij])

(iii) ( k + l) A = (k + l) [aij]

•  Multiplication of matrices - When two matrices A and B are multiplied, the number of columns in A  is equivalent to the total number of rows of B.

The entries in rows are multiplied by the corresponding entries in the columns; that is, the first row's entries are multiplied by the first column's entries, and so on.

(i) Non-commutativity of multiplication of matrices - Matrix multiplication is not commutative. if AB and BA are both defined, it is not necessary that AB = BA.

(ii) Zero matrix as the product of two non zero matrices - if the product of two matrices is a zero matrix, it is not necessary that one of the matrices is a zero matrix.

• Properties of multiplication of matrices - There are the properties of multiplication of matrices that we state without proof.

(i) The associative law - For any three matrices A, B and C. We have (AB) C = A (BC), whenever both sides of the equality are defined.

(ii) The distributive law -  For three matrices A, B and C.

(A) A (B+C) = AB + AC

(B) (ii) (A+B) C = AC + BC, whenever both sides of equality are defined.

(iii) The existence of multiplicative identity -  For every square matrix A, there exist an identity matrix of the same order such that IA = AI = A.

## Tips for Solving Exercise 3.2 Class 12 Chapter 3 Matrices

NCERT solutions class 12 maths chapter 3 ex 3.2 is a great way to practice matrices questions. Our expert team of mathematics have provided some useful tips to solve ex 3.2 with ease.

1. Students will quickly develop a thorough comprehension of any difficult concepts by using NCERT solutions for class 12 maths ch 3 ex 3.2 in practice. Students should start with the easier problems, to determine how much more practice they require for each area.

2. You must study and learn all the properties related to matrix operations to be well versed with the concepts.

3. If you get stuck on the complex problems, you can always access the step-by-step solutions provided by eSaral’s subject experts.

## Importance of Solving Ex 3.2 Class 12 Maths Chapter 3 Matrices

There are many important advantages given by experienced faculties of eSaral to help you solve questions of ex 3.2 class 12 maths chapter 3 Matrices.

1. Ex 3.2 class 12 maths chapter 3 describes operations on matrices, properties of scalar multiplication of a matrix, multiplication of matrices in detail that provides conceptual understanding. This will help you to solve questions of ex 3.2 quickly.

2. All the solutions of ex 3.2 are solved by expert teachers of eSaral in a precise manner that can help you write accurate answers in board exams.

3. Ex 3.2 class 12 maths solutions also provides examples and important questions related to the concepts that will clear your concepts step by step.

4. NCERT solutions PDF is made available here on eSaral that provides answers in simple language of all questions to score good marks in examinations.

Question 1. What are the properties of matrix addition?

1. Commutative Law

2. Associative Law

4. The existence of additive inverse

Question 2. What is Negative of a matrix?

Answer 2. When a matrix is multiplied by −1, the resultant matrix is negative.

Question 3. What is Difference of matrices?

Answer 3. It is only possible to subtract two matrices if their orders are the same. You can perform a subtraction by deducting the corresponding entries of two matrices.