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Chapter 3  ·  Class XII Mathematics  ·  MCQ Practice

MCQ Practice Arena

Matrices

Rows, Columns, Operations — Build Matrix Fluency for Every Exam

📋 50 MCQs ⭐ 26 PYQs ⏱ 85 sec/Q
🚀 Start Practising 📖 Revise Notes First

MCQ Bank Snapshot

50Total MCQs
16Easy
22Medium
12Hard
26PYQs
85 secAvg Time/Q
5Topics
Easy 32% Medium 44% Hard 24%

Why Practise These MCQs?

CBSE Class XIIJEE MainJEE Advanced

Matrices MCQs test whether you actually respect non-commutativity — most errors come from treating AB like BA. CBSE boards favour symmetric/skew-symmetric decomposition questions, while JEE mixes in invertibility and special-matrix identities. This bank is built to catch exactly those habits before the real exam does.

Topic-wise MCQ Breakdown

Matrix Basics & Types8 Q
Operations (Addition, Multiplication, Scalar)14 Q
Transpose & Symmetric/Skew-Symmetric10 Q
Invertible Matrices & Elementary Operations10 Q
Special Matrix Identities8 Q

Must-Know Formulae Before You Start

Recall these cold before attempting MCQs — they appear in >70% of questions.

$(AB)^T = B^T A^T$
$A = \dfrac{A+A^T}{2} + \dfrac{A-A^T}{2}$
$AA^{-1} = A^{-1}A = I$
$\text{Symmetric: } A^T=A; \text{ Skew-symmetric: } A^T=-A$

MCQ Solving Strategy

Always check dimensions before multiplying — mismatched matrices are an instant trap answer. When asked to write a matrix as symmetric + skew-symmetric parts, use the standard decomposition identity directly rather than solving from scratch. For invertibility, remember a matrix is invertible only if it's square and its determinant is non-zero.

⚠ Common Traps & Errors

Difficulty Ladder

Work through each rung in order — do not jump to Hard before mastering Easy.

① Easy

Identify matrix type, perform basic addition/scalar multiplication

② Medium

Matrix multiplication, transpose properties, symmetric/skew-symmetric checks

③ Hard

Prove matrix identities, find inverse via elementary operations

★ PYQ

JEE Main — matrix equation solving; CBSE — symmetric/skew-symmetric proofs

Continue Your Preparation

📖 Chapter Notes Revise concepts & theory 🧠 MCQ Practice Topic-wise Questions 🎯 PYQ Bank Previous year questions ✔️❌ True / False Concept-based True & False questions 📘✔️ Exercises Step by step Solutions to textbook exercises ➡ Next Chapter Determinants MCQs
🎯 Knowledge Check

Mathematics — Matrices

50 Questions Class 12 MCQs
1
Which of the following is a matrix of order \(2\times3\)?
2
If \(A=[a_{ij}]\) is a matrix of order \(3\times2\), then the number of elements in \(A\) is
3
Which of the following is a square matrix?
4
A matrix in which all elements are zero is called
5
The identity matrix of order \(3\) is
6
If \(A=\begin{bmatrix}2&3\\4&5\end{bmatrix}\), then \(A^T\) is
7
If \(A\) is a symmetric matrix, then
8
If \(A\) is a skew-symmetric matrix, then
9
The diagonal elements of a skew-symmetric matrix are always
10
If \(A\) and \(B\) are matrices of the same order, then \(A+B\) is obtained by
11
If \(A\) is of order \(2\times3\) and \(B\) is of order \(3\times4\), then \(AB\) is of order
12
If \(A\) is \(3\times2\) and \(B\) is \(2\times5\), then \(BA\) is
13
For matrices \(A\), \(B\), and \(C\) of compatible orders, which property is always true?
14
Matrix multiplication is generally
15
If \(A\) is a matrix of order \(m\times n\), then the order of \(A^T\) is
16
If \(A=\begin{bmatrix}1&2\\3&4\end{bmatrix}\) and \(B=\begin{bmatrix}2&1\\0&3\end{bmatrix}\), then \(A+B\) is
17
If \(A=\begin{bmatrix}1&2\\3&4\end{bmatrix}\), then \(2A-3I\) equals
18
If \(A=\begin{bmatrix}1&2\\0&1\end{bmatrix}\), then \(A^2\) is
19
If \(A=\begin{bmatrix}1&0\\2&3\end{bmatrix}\), then \(AI\), where \(I\) is the identity matrix of the same order, equals
20
If \(A\) and \(B\) are matrices such that \(AB\) is defined, then \((AB)^T\) equals
21
If \(A\) is symmetric and \(B\) is skew-symmetric, then \(A^T+B^T\) equals
22
If \(A=\begin{bmatrix}2&3\\3&5\end{bmatrix}\), then \(A\) is
23
If \(A=\begin{bmatrix}0&4\\-4&0\end{bmatrix}\), then \(A\) is
24
Every square matrix \(A\) can be expressed as
25
If \(A\) is a square matrix satisfying \(A^2=A\), then \(A\) is called
26
If \(A^2=I\), then \(A\) is called
27
If \(A^2=0\) for a non-zero square matrix \(A\), then \(A\) is
28
If \(A\) is invertible, then \(AA^{-1}\) is equal to
29
If \(A\) and \(B\) are invertible matrices of the same order, then \((AB)^{-1}\) is
30
If \(A\) is invertible, then \((A^{-1})^{-1}\) equals
31
If \(A=\begin{bmatrix}1&2\\3&4\end{bmatrix}\), then \(A^2-5A\) is
32
If \(A=\begin{bmatrix}1&2\\2&1\end{bmatrix}\), then \(A^2\) is
33
If \(A\) is symmetric and \(B\) is symmetric, then \(AB\) is symmetric if and only if
34
If \(A\) is symmetric and \(B\) is skew-symmetric, then \(AB\) is generally
35
If \(A=\begin{bmatrix}1&2\\2&4\end{bmatrix}\), which statement is correct?
36
If \(A=\begin{bmatrix}a&b\\c&d\end{bmatrix}\) is invertible, then \(A^{-1}\) is
37
The inverse of \(A=\begin{bmatrix}2&1\\1&1\end{bmatrix}\) is
38
If \(A=\begin{bmatrix}1&1\\0&1\end{bmatrix}\), then \(A^{-1}\) is
39
If \(A\) is invertible and \(AX=AY\), then
40
If \(A\) is invertible and \(AX=B\), then \(X\) is
41
If \(X A=B\), where \(A\) is invertible, then \(X\) is
42
If \(A\) and \(B\) are invertible matrices, then \(A^{-1}B^{-1}\) is equal to
43
If \(A^2-3A+2I=0\) and \(A\) is invertible, then \(A^{-1}\) is
44
If \(A^2-5A+6I=0\) and \(A\) is invertible, then \(A^{-1}\) equals
45
The system \(AX=B\) has a unique solution when
46
The solution of the matrix equation \(\begin{bmatrix}1&2\\2&3\end{bmatrix}X=\begin{bmatrix}5\\8\end{bmatrix}\) is
47
If \(A=\begin{bmatrix}1&2\\3&4\end{bmatrix}\), then \(A^{-1}\) is
48
If \(A\) is a square matrix such that \(A^T=A^{-1}\), then
49
If \(A\) and \(B\) are invertible matrices and \(AB=BA\), then \((AB)^{-1}\) can be written as
50
If \(A\) is an invertible matrix satisfying \(A^2-4A+3I=0\), then \(A^{-1}\) is
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Class 12 Matrices MCQs: 50 Questions with Answers
Class 12 Matrices MCQs: 50 Questions with Answers — Complete Notes & Solutions · academia-aeternum.com
Mastering NCERT Class 12 Mathematics Chapter 3 – Matrices is essential for building a strong foundation in algebra and preparing effectively for the CBSE Class 12 Mathematics Board Exam. This chapter introduces matrices as an organized way of representing numbers, equations, and mathematical relationships. Students will learn important concepts such as types of matrices, matrix operations, transpose of a matrix, symmetric and skew-symmetric matrices, matrix multiplication, elementary…
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Frequently Asked Questions

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.

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.

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.

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.

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.

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

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

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

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

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.

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

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.

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

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

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

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