Chapter 4 of the Class 12 NCERT Mathematics textbook is titled Determinants, and it builds directly on the previous chapter on matrices. This chapter teaches how to find the determinant of a matrix and use it in solving various types of mathematical problems. Determinants are useful in checking the invertibility of matrices and solving systems of linear equations. If you’re looking for the PDF of NCERT Chapter 4 – Determinants, you can download it easily for free and use it for regular practice and revision.
I’m writing about this topic because I’ve seen many students who are comfortable with matrices but get confused when it comes to determinants. But this chapter is quite logical and scoring once you understand the steps. Personally, I found that visualising the process of expanding determinants and applying properties made things much easier. Also, questions from this chapter regularly appear in board exams, especially 4- and 6-mark questions involving adjoint, inverse, and cofactor expansion. If you’re also preparing for competitive exams like JEE or CUET, a strong grip on this chapter can really help in quick problem solving. That’s why I think it’s important to explain the chapter clearly and guide students to the right NCERT PDF.
What You’ll Learn in NCERT Class 12 Chapter 4: Determinants
The chapter covers the basic definition and gradually moves to advanced applications of determinants in solving systems of equations. Here’s what the chapter includes:
- Definition of Determinant
Determinants of 1×1, 2×2, and 3×3 matrices explained with basic examples - Properties of Determinants
- Row or column interchange
- Scalar multiplication
- Addition of rows or columns
- Triangular form and other shortcuts
- Cofactor and Minors
How to find minors and cofactors of elements in a matrix - Adjoint and Inverse of a Matrix
Using cofactors to find the adjoint and then the inverse of a matrix - Application in Solving Equations
Using Cramer’s Rule to solve linear equations using determinants
These topics are explained with examples and the NCERT book provides a good mix of conceptual questions and exercises to practise.
Why You Should Pay Attention to Determinants
Determinants are not just a part of your syllabus — they are an essential tool in higher maths and engineering courses. In fact, the inverse of a matrix cannot be found unless its determinant is non-zero. So without understanding this chapter, you can’t go deeper into topics like vector algebra or calculus.
From a board exam point of view, this chapter usually carries 6 to 8 marks directly. If you memorise the properties and understand how to apply them, solving determinant-related questions becomes quite quick. You also avoid silly calculation mistakes. In competitive exams like JEE Main, questions involving Cramer’s rule and matrix inverse often come directly from NCERT.
