Class 12 Maths Chapter 3: Matrices – Concepts, NCERT Solutions & CBSE PYQs Explained
Here’s the comprehensive guide for Chapter 3: Matrices (Class 12 CBSE Maths): 🧠A. Key Concepts & Properties Matrix Definition & Order A matrix is a rectangular array [ a i j ] [a_{ij}] of order m × n m \times n containing real numbers/functions. Types of Matrices : Row , Column , Square , Rectangular Zero , Identity , Diagonal , Scalar Symmetric ( A T = A A^T = A ), Skew-symmetric ( A T = − A A^T = -A ), Transpose ( A T A^T ) Matrix Operations : Sum/Subtraction : Element-wise, requires same order Scalar Multiplication Matrix Multiplication : Product defined if columns of A = rows of B; not commutative . Elementary Row/Column Operations & Inverse : Inverse ( A − 1 A^{-1} ) exists only for square matrices; findable via elementary operations Properties of Transpose : ( A T ) T = A (A^T)^T = A , ( A B ) T = B T A T (AB)^T = B^T A^T Symmetric/Skew Decomposition : Any square A A can be writ...