Class 12 Maths Chapter 3 – Matrices NCERT Solutions – FREE PDF Download | Hand – Written Notes

Chapter 3 Matrices is one of the most important chapters of Class 12 Mathematics NCERT syllabus. This chapter introduces students to matrices, their types, operations, and applications. Matrices are widely used in higher mathematics, determinants, calculus, and real-life problems such as economics and engineering.

At Edu Tehri, this chapter is explained with clear concepts, step-by-step NCERT solutions, handwritten notes, important formulas, and free PDFs, helping students score better in board exams.

Important Topics of Chapter 3

The following important topics are included in NCERT Chapter 3 – Matrices:

1. Meaning and definition of matrices
2. Order of a matrix
3. Types of matrices
4. Zero matrix
5. Row matrix and column matrix
6. Square matrix
7. Diagonal, scalar, and identity matrices
8. Equality of matrices
9. Addition and subtraction of matrices
10. Multiplication of a matrix by a scalar
11. Multiplication of two matrices
12. Properties of matrix multiplication
13. Transpose of a matrix
14. Properties of transpose
15. Symmetric and skew-symmetric matrices

These topics are frequently asked in board exams and form the base for the next chapter Determinants.

Important Formulas – Chapter 3

Learning formulas is very important to score well in this chapter.

Basic Matrix Formulas

1. If A = [aᵢⱼ], then the order of A is m × n

2. Two matrices are equal if they have:
• Same order
• Corresponding elements equal Addition and Subtraction

3. A + B = [aᵢⱼ + bᵢⱼ]

4. A − B = [aᵢⱼ − bᵢⱼ]

(Only possible when matrices have the same order)

Scalar Multiplication

5. kA = [k × aᵢⱼ], where k is a real number

Matrix Multiplication

6. AB is defined only when:
• Number of columns of A = number of rows of B

7. (AB)ᵢⱼ = Σ aᵢₖ bₖⱼ

Properties of Matrix Multiplication

8. AB ≠ BA (Not commutative)
9. A(BC) = (AB)C (Associative)
10. A(B + C) = AB + AC

Transpose of a Matrix

11. If A = [aᵢⱼ], then Aᵀ = [aⱼᵢ]
12. (Aᵀ)ᵀ = A
13. (A + B)ᵀ = Aᵀ + Bᵀ
14. (AB)ᵀ = BᵀAᵀ

Symmetric and Skew-Symmetric Matrices

15. A is symmetric if Aᵀ = A
16. A is skew-symmetric if Aᵀ = −A

Exercises in Chapter 3

NCERT Chapter 3 consists of 2 exercises only.

Exercise List

1. Exercise 3.1, 3.2

There is no miscellaneous exercise in this chapter.

Exercise 3.1 – Basics of Matrices

This exercise covers:

• Definition and order of matrices
• Types of matrices
• Equality of matrices

Question Type:

• Find order
• Identify matrix type
• Solve simple matrix equations

Exam Weightage: Useful for 1–2 mark questions

Exercise 3.2 – Operations on Matrices

This exercise focuses on:

• Addition and subtraction
• Scalar multiplication
• Matrix multiplication
• Transpose and its properties

Question Type:

• Numerical problems
• Proving properties
• Long answer questions

Exam Weightage: Very high for 3–5 mark questions

6. Key Features of Chapter 3

• Concept-based chapter
• Foundation for determinants
• Frequently asked in board exams
• Mix of theory and numericals
• Requires regular practice

With Edu Tehri’s structured notes and solutions, students can easily master matrices.

Frequently Asked Questions (Long Answer Type – NCERT Based)

Q1. What is a matrix?

A matrix is a rectangular arrangement of numbers, symbols, or expressions arranged in rows and columns.

Q2. What is the order of a matrix?

The order of a matrix is written as m × n, where m is the number of rows and n is the number of columns.

Q3. When are two matrices equal?

Two matrices are equal when they have the same order and their corresponding elements are equal.

Q4. Can we add two matrices of different order?

No, matrix addition is possible only when both matrices have the same order.

Q5. Is matrix multiplication commutative?

No, matrix multiplication is not commutative, meaning AB ≠ BA in general.

Q6. What is an identity matrix?

An identity matrix is a square matrix in which all diagonal elements are 1 and all other elements are 0.

Q7. What is the transpose of a matrix?

The transpose of a matrix is obtained by interchanging rows and columns.

Q8. What is a symmetric matrix?

A matrix is symmetric if its transpose is equal to the matrix itself.

Q9. Why is Chapter 3 important for exams?

Matrices form the base for determinants and carry high weightage in board exams.

Q10. Where can students get free NCERT solutions for Matrices?

Students can get complete NCERT solutions, handwritten notes, and free PDFs on Edu Tehri.

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