Skip to main content
Super TutorResources
Chapter 5 of 13
Concept Maps

Matrices — Concept Maps

ICSE · Class 12 · Mathematics

4 concept maps of Matrices for ICSE Class 12 Mathematics, each also written out as a text outline. Part of the ICSE Class 12 Mathematics syllabus.

97 questions32 flashcards18 formulas & key relations5 concepts

Interactive on Super Tutor

Studying Matrices? Get the full interactive chapter.

Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for concept maps and more.

Try Super Tutor — Free

Free trial, no card needed.

A visual representation of a matrix, clearly showing its elements, rows, columns, and how its order (m x n) is defined. Highlight the 'a_ij' notation for elements.
Super Tutor

One of 11 illustrations for Matrices in Super Tutor — alongside flashcards, concept maps and practice questions.

4 Concept Maps

Complete Mind Map of Matrices Chapter

Complete Mind Map of Matrices Chapter

The map in words

  • Matrices
    • Basic Concepts
      • Definition
        • Rectangular array
        • Rows and columns
      • Order m x n
        • m rows n columns
        • Total elements = mn
      • Element notation
        • aij = row i col j
    • Types of Matrices
      • Zero Matrix O
      • Row Matrix 1 x n
      • Column Matrix m x 1
      • Square Matrix m = n
        • Diagonal elements
        • Trace = sum of diagonal
      • Special Square
        • Diagonal Matrix
        • Scalar Matrix
        • Identity Matrix
        • Upper Triangular
        • Lower Triangular
    • Operations
      • Addition A + B
        • Same order required
        • Add corresponding elements
      • Subtraction A - B
        • Same order required
      • Scalar Multiplication kA
        • Multiply all elements by k
      • Matrix Multiplication AB
        • Columns of A = Rows of B
        • Order of AB = m x p
        • Not commutative
    • Transpose
      • Definition
        • Swap rows and columns
      • Properties
        • Transpose of transpose = A
        • AB transpose = BT AT
        • Order reverses
    • Symmetric and Skew
      • Symmetric AT = A
      • Skew AT = negative A
        • Diagonal = 0
      • Decomposition
        • P = half A + AT
        • Q = half A - AT
    • Inverse
      • AB = BA = I
      • Unique inverse
      • AB inverse = B inv A inv
      • From polynomial equation
      • By Elementary Transformations
        • Row method A = IA
        • Column method A = AI

Matrix Concepts Hierarchy

Matrix Concepts Hierarchy

The map in words

  • MATRICES
    • Definition and Order
      • Rows and Columns
      • Element Notation aij
      • m x n Order
    • Types of Matrices
      • Zero Matrix
      • Row and Column
      • Square Matrix
      • Diagonal Matrix
      • Scalar Matrix
      • Identity Matrix
      • Triangular Matrices
    • Operations
      • Addition
      • Subtraction
      • Scalar Multiplication
      • Matrix Multiplication
    • Properties
      • Transpose
      • Symmetric Matrix
      • Skew-symmetric Matrix
    • Inverse and Transformations
      • Matrix Inverse
      • Invertibility Conditions
      • Elementary Row Operations
      • Elementary Column Operations
      • Row Reduction Method
    • Applications
      • Cryptography
      • Computer Graphics
      • Physics and Engineering
      • Data Analysis

Matrices - Comprehensive Concept Map

Matrices - Comprehensive Concept Map

The map in words

  • MATRICES
    • Fundamentals
      • Order and Elements
      • Types of Matrices
        • Null Matrix
        • Row Matrix
        • Column Matrix
        • Square Matrix
        • Diagonal Matrix
        • Scalar Matrix
        • Identity Matrix
    • Operations
      • Addition
        • Same order required
        • Element-wise
      • Subtraction
        • Same order required
        • A - B = A + (-B)
      • Scalar Multiplication
        • k × A
        • All elements multiplied
    • Matrix Multiplication
      • Conditions
        • Columns of A = Rows of B
        • Result order m × p
      • Properties
        • NOT commutative
        • Associative
        • Distributive
    • Transpose
      • (A^T)^T = A
      • (A + B)^T = A^T + B^T
      • (AB)^T = B^T A^T
    • Special Matrices
      • Symmetric A^T = A
      • Skew-symmetric A^T = -A
      • Involution A^2 = I
      • Idempotent A^2 = A
    • Inverse
      • Exists if square and det(A) ≠ 0
      • AA^(-1) = I
      • Finding methods
        • 2×2 formula
        • Elementary operations
    • Applications
      • Business problems
      • Linear systems
      • Transformations

Matrices as rectangular arrays used for representation, operations, special types, transpose, symmetry, and inverse

Matrices as rectangular arrays used for representation, operations, special types, transpose, symmetry, and inverse

The map in words

  • Matrices as rectangular arrays used for representation, operations, special types, transpose, symmetry, and inverse
    • Matrix
    • Order of a matrix
    • Types of matrices
    • Equality of matrices
    • Matrix operations
    • Properties of matrix addition
    • Properties of scalar multiplication
    • Properties of matrix multiplication

Explore these maps interactively

Explore Diagrams

Frequently Asked Questions

What are the important topics in Matrices for ICSE Class 12 Mathematics?
Key topics in Matrices include Basic concepts and types of matrices, Equality, addition, subtraction, and scalar multiplication, Multiplication of matrices and matrix polynomials, Transpose of a matrix. Study these first, then practise questions on each for the ICSE Class 12 board exam.
What do the concept maps for Matrices show?
The 4 maps show how the ideas in Matrices connect: Complete Mind Map of Matrices Chapter; Matrix Concepts Hierarchy. Each map is also written out as an outline on this page.
How should I revise Matrices for the ICSE Class 12 board exam?
Learn the core ideas first, then work through the 97 practice questions on Matrices. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

More resources for Matrices

All ICSE Class 12 Mathematics Concept Maps

For serious students

Get the full Matrices chapter — start free.

Quizzes, flashcards, an AI doubt solver and a study plan for ICSE Class 12 Mathematics. Free to start, no card needed.

Try Super Tutor Free
Try this chapter free