Matrices MCQ with Solutions

Hi, let’s quickly go through the NCERT Class 12 Matrices MCQ. These questions will help you revise the key ideas of this chapter in very little time. I’ve also added video solutions, so if you get stuck, you can watch the step-by-step explanation.

Quick Links

Ready? Okay, let’s begin with the first multiple choice question!

Matrices MCQ#1 (NCERT Exercise 3.1 – Question 8)

📍A given matrix $A=[a_{ij}]_{m\times n} \text{ is a square matrix, if }$

Options:

(A) $m<n$
(B) $m>n$
(C) $m=n$
(D) None of these

Answer:
✅ Correct option: (C) $m=n$

Explanation:

A matrix is square when the number of rows equals the number of columns, i.e., $m=n$ .

Watch Video Solution on YouTube

Matrices MCQ#2 (NCERT Exercise 3.1 – Question 9)

📍Which of the given values of $x$ and $y$ make the following pair of matrices equal?

$\left[ \begin{array}{cc} 3x+7 & 5 \\ y+1 & 2-3x \end{array} \right] = \left[ \begin{array}{cc} 0 & y-2 \\ 8 & 4 \end{array} \right]$

Options:

(A) $x=-\tfrac{1}{3}; y=7$
(B) Not possible to find
(C) $y=7; x=-\tfrac{2}{3}$
(D) $x=-\tfrac{1}{3}; y=-\tfrac{2}{3}$

Answer:
✅ Correct option: (B) Not possible to find

Explanation:

For two matrices to be equal, each corresponding entry must be equal.

From top-left: $3x+7=0 \Rightarrow x=-\tfrac{7}{3}$
From bottom-right: $2-3x=4 \Rightarrow -3x=2 \Rightarrow x=-\tfrac{2}{3}$

The two values of $x$ do not match, so there is no common solution.

Watch Video Solution on YouTube

If you have been following this website as a resource for some of the important questions. For example, how to Integrate Square Root of tan x, or may be a complete guide to look at using Matrix Method in solving a system of linear equations. Trust me, this series on NCERT Class 12 MCQs is going to help you in many ways.

Moving onto the next Matrices MCQ in this part of the series.

Matrices MCQ#3 (NCERT Exercise 3.1 – Question 10)

📍The number of all possible matrices of order $3\times 3$ with each entry 0 or 1 is:

Options:

(A) 27
(B) 18
(C) 81
(D) 512

Answer:
✅ Correct option: (D) 512

Explanation:

A $3\times 3$ matrix has 9 entries.
Each entry has 2 choices (0 or 1).
Total matrices $= 2^{9} = 512$

Watch Video Solution on YouTube

Matrices MCQ#4 (NCERT Exercise 3.2 – Question 21)

📍Assume $X, Y, Z, W \text{ and } P$ are matrices of order
$2 \times n, 3 \times k, 2 \times p, n \times 3 \text{ and } p \times k$ , respectively. (This is for Matrices MCQ#4 and MCQ#5)

The restriction on $n, k \text{ and } p$ so that $PY + WY$ will be defined are:

Options:

(A) $k=3, p=n$
(B) $k \text{ is arbitrary}, p=2$
(C) $p \text{ is arbitrary}, k=3$
(D) $k=2, p=3$

Answer:
✅ Correct option: (A) $k=3, p=n$

Explanation:

$Y$ is of order $3 \times k$

And $P$ is of order $p \times k$ , so $PY$ is defined if $k=3$ , giving order $p \times k \Rightarrow p \times 3$ .

Whereas, $W$ is of order $n \times 3$ , so $WY$ is defined if $k=3$ , giving order $n \times k \Rightarrow n \times 3$ .

For addition $PY + WY$ to be defined, their orders must be the same.
So, $p=n$ and $k=3$ .

Watch Video Solution on YouTube

Matrices MCQ#5 (NCERT Exercise 3.2 – Question 22)

📍Assume $X, Y, Z, W \text{ and } P$ are matrices of order
$2 \times n; 3 \times k; 2 \times p; n \times 3 \text{ and } p \times k$ , respectively. (This is for Matrices MCQ#4 and MCQ#5)

The restriction on $n, k \text{ and } p$ so that $PY + WY$ will be defined are:

Options:

(A) $p \times 2$
(B) $2 \times n$
(C) $n \times 3$
(D) $p \times n$

Answer:
✅ Correct option: (B) $2 \times n$

Explanation:

$X$ is of order $2 \times n$ .

And $Z$ is of order $2 \times p$ .

If $n=p$ , then both $X$ and $Z$ have the same order $2 \times n$ .

So $7X - 5Z$ is defined, and its order is $2 \times n$ .

Watch Video Solution on YouTube

Let me tell you all of these 11 Matrices MCQ are so simple and easy to understand and so are scoring too. But then as they say, Math requires practice. So, my suggestion to you is to practice these NCERT Matrices MCQ a good number of times and feel confident. And if you ever need any clarification, just drop a comment — I’ll be more than happy to help.

Matrices MCQ#6 (NCERT Exercise 3.3 – Question 11)

📍If $A, B$ are symmetric matrices of same order, then $AB - BA$ is a:

Options:

(A) Skew symmetric matrix
(B) Symmetric matrix
(C) Zero matrix
(D) Identity matrix

Answer:
✅ Correct option: (A) Skew symmetric matrix

Explanation:

For any matrices $A, B$ ,
$(AB - BA)' = B'A' - A'B'$

Since $A, B$ are symmetric, $A'=A; B'=B$

So $(AB - BA)' = BA - AB = -(AB - BA)$

That means $AB - BA$ is skew symmetric.

Watch Video Solution on YouTube

Matrices MCQ#7 (NCERT Exercise 3.3 – Question 12)

📍If $A = \left[ \begin{array}{cc} \cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha \end{array} \right]$ and $A + A' = I$ , then the value of $\alpha$ is:

Options:

(A) $\tfrac{\pi}{6}$
(B) $\tfrac{\pi}{3}$
(C) $\pi$
(D) $\tfrac{3\pi}{2}$

Answer:
✅ Correct option: (B) $\tfrac{\pi}{3}$

Explanation:

$A = \left[ \begin{array}{cc} \cos\alpha & -\sin\alpha \\ \sin\alpha & \cos\alpha \end{array} \right]$

And $A' = \left[ \begin{array}{cc} \cos\alpha & \sin\alpha \\ -\sin\alpha & \cos\alpha \end{array} \right]$

So, $A + A' = \left[ \begin{array}{cc} 2\cos\alpha & 0 \\ 0 & 2\cos\alpha \end{array} \right] = 2\cos\alpha\, I$

$\text{Given }A+A'=I \Rightarrow 2\cos\alpha = 1 \Rightarrow \cos\alpha = \tfrac{1}{2}$

$\therefore\; \alpha = \tfrac{\pi}{3}$

Watch Video Solution on YouTube

Matrices MCQ#8 (NCERT Exercise 3.4 – Question 1)

📍Matrices $A \text{ and } B$ will be inverse of each other only if:

Options:

(A) $AB = BA$
(B) $AB = BA = 0$
(C) $AB = 0, BA = I$
(D) $AB = BA = I$

Answer:
✅ Correct option: (D) $AB = BA = I$

Explanation:

By definition, $B$ is the inverse of $A$ if $AB = BA = I$ .

Just $AB = I$ or $BA = I$ alone is not sufficient in general for matrices.

Therefore, both conditions must hold: $AB = BA = I$ .

Watch Video Solution on YouTube

You know there are about 100 MCQs in NCERT textbooks for Class 12 (both Part 1 and Part 2). I shall be taking one Chapter at a time and show you the explanations for each of the questions. Moreover, I have also covered these solutions in the video form and they are freely available on my YouTube channel, @Mathsbetter. And here also, in each of the 11 Matrices MCQ on this page, I have provided the direct links to each and every MCQ for you to understand the solutions in a very simple and easy manner.

Matrices MCQ#9 (NCERT Miscellaneous Exercise – Question 9)

📍If $A = \left[ \begin{array}{cc} \alpha & \beta \\ \gamma & -\alpha \end{array} \right]$ , is such that $A^2 = I$ , then:

Options:

(A) $1 + \alpha^2 + \beta\gamma = 0$
(B) $1 - \alpha^2 + \beta\gamma = 0$
(C) $1 - \alpha^2 - \beta\gamma = 0$
(D) $1 + \alpha^2 - \beta\gamma = 0$

Answer:
✅ Correct option: (C) $1 - \alpha^2 - \beta\gamma = 0$

Explanation:

$A^2 = \left[ \begin{array}{cc} \alpha & \beta \\ \gamma & -\alpha \end{array} \right] \left[ \begin{array}{cc} \alpha & \beta \\ \gamma & -\alpha \end{array} \right] = \left[ \begin{array}{cc} \alpha^{2} + \beta\gamma & 0 \\ 0 & \alpha^{2} + \beta\gamma \end{array} \right]$

So, $\left[ \begin{array}{cc} \alpha^{2} + \beta\gamma & 0 \\ 0 & \alpha^{2} + \beta\gamma \end{array} \right] = \left[ \begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array} \right] \quad \text{(since }A^2=I\text{)}$

$\alpha^{2} + \beta\gamma = 1 \;\Rightarrow\; 1 - \alpha^{2} - \beta\gamma = 0$

Watch Video Solution on YouTube

Matrices MCQ#10 (NCERT Miscellaneous Exercise – Question 10)

📍If the matrix $A$ is both symmetric and skew symmetric, then:

Options:

(A) $A \text{ is a diagonal matrix}$
(B) $A \text{ is a zero matrix}$
(C) $A \text{ is a square matrix}$
(D) None of these

Answer:
✅ Correct option: (B) $A \text{ is a zero matrix}$

Explanation:

We know that, if $A$ is symmetric, then $A' = A$ .

And if $A$ is skew symmetric, then $A' = -A$ .

Both together give $A = -A \Rightarrow 2A = 0 \Rightarrow A = 0$ .

Watch Video Solution on YouTube

Matrices MCQ#11 (NCERT Miscellaneous Exercise – Question 11)

📍If $A$ is a square matrix such that $A^2 = A$ , then $(I + A)^3 - 7A$ is equal to:

Options:

(A) $A$
(B) $I - A$
(C) $I$
(D) $3A$

Answer:
✅ Correct option: (C) $I$

Explanation:

Expand: $(I + A)^3 = I^3 + 3I^2A + 3IA^2 + A^3$

$= I + 3A + 3A^2 + A^3$

Since $A^2 = A$ , we have $A^3 = A^2 = A$

So $(I + A)^3 = I + 3A + 3A + A = I + 7A$

Then $(I + A)^3 - 7A = (I + 7A) - 7A = I$

Watch Video Solution on YouTube

Quick Answer Key

Here is the complete Matrices MCQ Quick Revision Key for your reference.

Q1 → (C)
Q2 → (B)
Q3 → (D)
Q4 → (A)
Q5 → (B)
Q6 → (A)
Q7 → (B)
Q8 → (D)
Q9 → (C)
Q10 → (B)
Q11 → (C)

Closing Note

That completes all the important NCERT Class 12 Maths Matrices MCQ from chapter 3.
I hope the explanations and video solutions made things clearer and gave you more confidence. Stay tuned for the next chapter, where we’ll cover all the important Determinants MCQ with the same clarity and video support.

👉 Tip: Try solving these questions again tomorrow without looking at the answers. You’ll see how much sharper your recall gets with each attempt.

Keep practicing — every time you do, you get one step closer to making you maths better!
You’re doing great, keep it up 🚀

Discover more from Maths Better

Subscribe to get the latest posts sent to your email.

Matrices MCQ#1 (NCERT Exercise 3.1 – Question 8)

Matrices MCQ#2 (NCERT Exercise 3.1 – Question 9)

Matrices MCQ#3 (NCERT Exercise 3.1 – Question 10)

Matrices MCQ#4 (NCERT Exercise 3.2 – Question 21)

Matrices MCQ#5 (NCERT Exercise 3.2 – Question 22)

Matrices MCQ#6 (NCERT Exercise 3.3 – Question 11)

Matrices MCQ#7 (NCERT Exercise 3.3 – Question 12)

Matrices MCQ#8 (NCERT Exercise 3.4 – Question 1)

Matrices MCQ#9 (NCERT Miscellaneous Exercise – Question 9)

Matrices MCQ#10 (NCERT Miscellaneous Exercise – Question 10)

Matrices MCQ#11 (NCERT Miscellaneous Exercise – Question 11)

Quick Answer Key

Closing Note

Share this:

Discover more from Maths Better

Related Posts

Your Words Matter!Cancel reply

Discover more from Maths Better

Discover more from Maths Better