Matrices Class 12 – CBSE 2025 Complete Guide | Notes, Formulas, Questions

The Matrices chapter in CBSE Class 12 Mathematics is a crucial part of the Algebra section. It lays the groundwork for complex calculations in fields like Engineering, Computer Science, and Data Analysis. This guide will help you understand all the important concepts, types, formulas, and operations of matrices in a student-friendly format.

🔹 What is a Matrix?

A matrix is a rectangular arrangement of numbers, symbols, or expressions in rows and columns. It is widely used in linear algebra, programming, and real-world applications like economics, cryptography, and graphics transformations.

📖 Matrix Notation

A matrix with m rows and n columns is called an m × n matrix. Example: A = [[1, 2], [3, 4]] is a 2×2 matrix.

🔹 Types of Matrices

• Row Matrix
• Column Matrix
• Zero (Null) Matrix
• Diagonal Matrix
• Scalar Matrix
• Identity Matrix
• Symmetric and Skew-Symmetric Matrices

🔹 Matrix Operations

• Addition and Subtraction of Matrices
• Multiplication by a Scalar
• Matrix Multiplication
• Transpose of a Matrix
• Properties of Matrix Operations

🔹 Key Formulas & Properties

• \((A^T)^T = A\)
• \((A + B)^T = A^T + B^T\)
• \((AB)^T = B^T \cdot A^T\)
• \(A \cdot I = I \cdot A = A\) (where I is the Identity Matrix)
• If \(A^2 – 5A + 6I = 0\), then \(A^{-1} = \frac{1}{6}(5I – A)\)

🔹 Board Exam Style Questions

• 1 Mark: Define a diagonal matrix.
• 2 Marks: Show \(A^2 = -I\) for a given matrix.
• 3 Marks: Multiply two matrices and verify \(AB ≠ BA\).
• 4 Marks: Prove \((A + A^T)^T = A + A^T\).

🔹 Tips to Score Full Marks

• Learn matrix types with examples.
• Practice non-commutative matrix multiplication.
• Revise transpose and inverse properties regularly.
• Use clean steps in your answers for maximum marks.

🔹 Practice Worksheet

We’ve created a full worksheet for Class 12 students based on board exam style:

• 16 practice questions
• From 1-mark to 4-mark levels
• Includes HOTS (Higher Order Thinking Skills)
• Designed per CBSE 2025 blueprint

👉 Click here to view the full worksheet

🧠 Final Thoughts

Matrices are essential not only for CBSE exams but also for entrance exams and real-world applications. Strengthen your basics, practice consistently, and stay confident. This guide + worksheet combo is your key to scoring full marks!