ICSE Class 10 Maths: Matrices — Complete Chapter Notes 2026

Introduction to Matrices

• Matrix: rectangular array of numbers arranged in rows and columns; denoted by capital letters A, B, C
• Order of a matrix: m × n where m = rows, n = columns; a 3×2 matrix has 3 rows, 2 columns
• Element notation: aᵢⱼ is element in i-th row and j-th column

Types of Matrices

• Row matrix: 1×n; Column matrix: m×1; Square matrix: m×n where m = n
• Null/Zero matrix: all elements = 0; Identity matrix: square matrix with 1s on diagonal, 0s elsewhere
• Diagonal matrix: all non-diagonal elements are 0; Symmetric: A = Aᵀ

Matrix Addition and Subtraction

• Only matrices of same order can be added/subtracted; add corresponding elements
• Addition is commutative: A + B = B + A; and associative: (A + B) + C = A + (B + C)
• Scalar multiplication: kA multiplies every element of A by scalar k

Matrix Multiplication

• A(m×n) × B(n×p) = C(m×p); number of columns of A must equal number of rows of B
• Not commutative: AB ≠ BA in general; is associative: (AB)C = A(BC)
• cᵢⱼ = sum of (aᵢₖ × bₖⱼ) for k = 1 to n; each element is dot product of row and column

Transpose of a Matrix

• Transpose Aᵀ: rows become columns; (Aᵀ)ᵀ = A; (A+B)ᵀ = Aᵀ + Bᵀ
• For symmetric matrix A: A = Aᵀ; for skew-symmetric: A = −Aᵀ
• (AB)ᵀ = BᵀAᵀ (reverse order for transpose of product)

ICSE Syllabus Scope

• ICSE Class 10: 2×2 and 2×1 matrices only; no determinants or inverse at this level
• Typical question: given matrix equations, find unknown matrix elements
• Application: solving simultaneous equations using matrix method not required at ICSE 10 level

Common Mistakes

• Multiplying matrices of incompatible orders — always check order compatibility first
• Forgetting AB ≠ BA; writing AB when BA was required in the question
• Wrong transpose: students often forget to swap rows and columns completely