Class 12MathematicsChapter 3: Matrices

Key Formulas

Summary of key formulas for matrices.

Concept	Formula
Matrix product entry	$(AB)_{ij} = \sum_{k=1}^{n} a_{ik} b_{kj}$
Transpose product	$(AB)^T = B^T A^T$
Symmetric decomposition	$A = \frac{1}{2}(A + A^T) + \frac{1}{2}(A - A^T)$
$2 \times 2$ inverse	$A^{-1} = \frac{1}{ad-bc}\begin{bmatrix} d & -b \\ -c & a \end{bmatrix}$

3.5 Invertible Matrices

Definition of inverse, 2x2 inverse formula, and worked example.

7.1 Introduction

Integration as the inverse process of differentiation and the constant of integration.