Class 12 Mathematics Chapter 4 Determinants – Revision Notes

Quick revision notes for Class 12 Maths Chapter 4 (Determinants). These Class 12 Mathematics Chapter 4 notes are ideal for quick revision just before exams.

Determinant Basics

• 2×2: |A|=ad−bc.
• 3×3: expand via cofactors along any row/column.
• Singular matrix: |A|=0, no inverse exists.

Properties

• |A’|=|A|; swapping rows/cols flips sign; identical rows/cols give |A|=0; |AB|=|A||B|.

Applications

• Area of triangle via determinant formula.
• A⁻¹=adj(A)/|A| (|A|≠0 required).
• Matrix method: AX=B ⇒ X=A⁻¹B.

One-Line Summary

The determinant is a scalar characterizing a square matrix’s invertibility, used to compute inverses, areas, and to solve linear systems via the matrix method.

Written by Satish

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