What is a matrix in Class 12 Mathematics?

A matrix is an ordered rectangular array of numbers or functions arranged in rows and columns. The individual numbers or functions are called elements or entries.

What is the order of a matrix?

The order of a matrix is written as m × n, where m represents the number of rows and n represents the number of columns. An m × n matrix contains mn elements.

What are the different types of matrices in Class 12?

Important types include row matrix, column matrix, rectangular matrix, square matrix, zero matrix, diagonal matrix, scalar matrix and identity matrix. Symmetric and skew-symmetric matrices are also important.

When are two matrices equal?

Two matrices are equal when they have the same order and every corresponding element is equal. Thus, A = B if aij = bij for all valid i and j.

When is matrix multiplication possible?

If A is of order m × n and B is of order n × p, then AB is defined and has order m × p. The number of columns of the first matrix must equal the number of rows of the second matrix.

Is matrix multiplication commutative?

Generally, matrix multiplication is not commutative. In general, AB ? BA. Moreover, one product may be defined while the other may not be defined.

What is the transpose of a matrix?

The transpose of a matrix is obtained by interchanging its rows and columns. If A = [aij]m × n, then A' = [aji]n × m.

What is a symmetric matrix?

A square matrix A is symmetric if A' = A. Equivalently, its corresponding elements satisfy aij = aji for all i and j.

What is a skew-symmetric matrix?

A square matrix A is skew-symmetric if A' = -A. Consequently, every diagonal element of a skew-symmetric matrix is zero.

What is an invertible matrix and its inverse?

A square matrix A is invertible if there exists a matrix A?¹ of the same order such that AA?¹ = A?¹A = I. The inverse, when it exists, is unique.

What is Chapter 3 of NCERT Class 12 Mathematics?

Chapter 3 is Matrices, which covers types of matrices, matrix operations, transpose, symmetric and skew-symmetric matrices, matrix multiplication, and inverse of a matrix.

What are the main topics covered in Matrices?

The main topics include types of matrices, equality of matrices, matrix operations, transpose, symmetric and skew-symmetric matrices, elementary properties, and inverse of a matrix.

Are these Matrices MCQs based on the NCERT syllabus?

Yes, these MCQs are based on the concepts covered in the NCERT Class 12 Mathematics Chapter 3 Matrices syllabus.

How many Matrices MCQs are included in this practice set?

This practice set contains 50 multiple-choice questions with answers and concise explanations.

Are these MCQs useful for CBSE Board Exam preparation?

Yes, practising these MCQs can help strengthen concepts, improve accuracy, and support CBSE Class 12 Mathematics Board Exam preparation.

Class 12 Matrices | NCERT Maths Chapter 3 Notes & Solutions

10 CBSE Marks

★★★★★ Difficulty

8 Topics

High JEE Weight

Topics Covered

8 key topics in this chapter

Matrix Notation & Order

Types of Matrices

Equality of Matrices

Addition, Subtraction & Scalar Multiplication

Multiplication of Matrices

Transpose of a Matrix

Symmetric & Skew-Symmetric Matrices

Elementary Operations & Invertible Matrices

Study Resources

📖 NCERT Notes ✏️ MCQ Practice 🏆 JEE / CBSE PYQs 📝 Exercise Solutions ✅ True / False Quiz

𝑓 Key Formulae

Essential mathematical expressions for this chapter — understand derivations, not just results.

Order of a Matrix

\[A_{m \times n} \text{ has } m \text{ rows},\, n \text{ columns}\]

📌 Total entries = m·n

Symmetric Matrix

\[A' = A\]

📌 Equal to its own transpose

Skew-Symmetric Matrix

\[A' = -A\]

📌 Diagonal entries must all be zero

Sum Decomposition

\[A = \tfrac{1}{2}(A+A') + \tfrac{1}{2}(A-A')\]

📌 Any square matrix splits into symmetric + skew-symmetric

Transpose of Product

\[(AB)' = B'A'\]

📌 Order reverses on transpose

🎯 Exam-Ready Insights

Important points to remember — curated from CBSE Board question patterns.

CBSE frequently asks to express a given square matrix as the sum of a symmetric and a skew-symmetric matrix — the decomposition formula is a guaranteed 3–5 mark question.

Matrix multiplication is defined only when the number of columns of the first equals the number of rows of the second — always state compatibility before multiplying.

Matrix multiplication is not commutative in general (AB ≠ BA), even when both products are defined.

Elementary row/column operations are used to find the inverse — practise the step-by-step reduction to identity.

🏆 Competitive Exam Strategy

Targeted tips for JEE Main, JEE Advanced, NEET, BITSAT, and CBSE Boards.

JEE Main

Idempotent, involutory, and nilpotent matrix properties (A²=A, A²=I, Aⁿ=0) are tested through direct verification — compute and check rather than memorising results.

JEE Advanced

Matrix equations combined with determinant conditions for singular/non-singular cases are a recurring problem type.

BITSAT

2×2 and 3×3 matrix multiplication under time pressure — practise mental row-column dot products.

⚠️ Common Mistakes to Avoid

Multiplying matrices in the wrong order or without checking column–row compatibility.

Assuming AB = BA — matrix multiplication is generally non-commutative.

Confusing transpose (swap rows/columns) with inverse (a completely different operation).

💡 Key Takeaways

◆

A matrix is simply a rectangular arrangement of numbers; its order (rows × columns) governs which operations are valid.

◆

Addition and scalar multiplication are entry-wise; multiplication is row-by-column.

◆

A square matrix is invertible only if its determinant is non-zero.

Matrices