NCERT Class 12 Mathematics Mathematics Part-I: Chapter 4 — MATHEMATICS
This chapter, Determinants, introduces the concept of determinants as a number associated with every square matrix. It explains how determinants are used to determine the uniqueness of solutions for systems of linear equations. The chapter covers the definition of determinants for matrices of order one, two, and three, along with methods for their calculation. It also highlights the wide applications of determinants in various fields like Engineering, Science, and Economics. Students will learn about properties of determinants, minors, cofactors, and their use in finding the area of a triangle, the adjoint and inverse of a square matrix, and solving systems of linear equations. This foundational knowledge is crucial for advanced mathematical concepts in CBSE Class 12 Mathematics.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 12 |
| Subject | Mathematics |
| Book | Mathematics Part-I |
| Chapter | Chapter 4 — MATHEMATICS |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 4 minutes |
| Word count | 655 |
Learning outcomes
- Understand the definition and notation of determinants for square matrices.
- Calculate determinants for matrices of order 1, 2, and 3.
- Recognize the association of determinants with the uniqueness of solutions for linear equations.
- Learn about minors and cofactors of determinant elements.
- Be introduced to the applications of determinants in geometry and algebra.
Vocabulary
| Word | Meaning |
|---|---|
| Determinant | A number associated with every square matrix. |
| Square matrix | A matrix with an equal number of rows and columns. |
| Order of a matrix | The number of rows or columns in a square matrix. |
| Unique solution | A system of equations having only one possible answer. |
| Minor | The determinant of a submatrix obtained by deleting a row and column. |
| Cofactor | A minor multiplied by (-1)^(i+j). |
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Practice questions
- What is the determinant of a 1x1 matrix A = [a]? Answer: The determinant is 'a'.
- Evaluate the determinant of the matrix [[2, 4], [-1, 2]]. Answer: 8
- For a matrix A = [[a, b], [c, d]], what is its determinant? Answer: |A| = ad - bc
Practice MCQs
Q1. What is the determinant of the matrix A = [5]?
Explanation: The determinant of a 1x1 matrix [a] is simply the element 'a'.
Q2. If A = [[a, b], [c, d]], then det(A) is:
Explanation: The determinant of a 2x2 matrix is calculated as the product of the main diagonal elements minus the product of the off-diagonal elements.
Q3. Which of the following is NOT a notation for the determinant of matrix A?
Explanation: While |A|, det A, and ∆ are common notations, 'Determinant(A)' is not a standard mathematical notation.
Q4. Determinants are associated with which type of matrices?
Explanation: Determinants are defined only for square matrices, which have an equal number of rows and columns.
Q5. The expression a1 b2 – a2 b1 is associated with the determinant of which matrix?
Explanation: The expression a1 b2 – a2 b1 corresponds to the determinant of the matrix [[a1, b1], [a2, b2]].
Frequently asked questions
What is a determinant?
A determinant is a scalar value that can be computed from the elements of a square matrix. It provides important information about the matrix and the system of linear equations it represents.
Can determinants be calculated for any matrix?
No, determinants can only be calculated for square matrices (matrices with an equal number of rows and columns).
What is the determinant of a 1x1 matrix A = [a]?
The determinant of a 1x1 matrix A = [a] is simply the value 'a'.
How is the determinant of a 2x2 matrix A = [[a, b], [c, d]] calculated?
The determinant is calculated as ad - bc.
What does the determinant tell us about a system of linear equations?
The determinant of the coefficient matrix indicates whether a system of linear equations has a unique solution (if the determinant is non-zero) or not.
What are minors and cofactors in the context of determinants?
A minor is the determinant of a submatrix formed by deleting one row and one column. A cofactor is the minor multiplied by (-1)^(i+j), where i and j are the row and column indices.
Related resources
Important topics
Topics covered
NCERT Class 12 Mathematics — Mathematics Part-I — Chapter 4 — MATHEMATICS. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.