If $A=\begin{bmatrix} 2 & 0 \\ 0 & 2 \end{bmatrix}$, then $A^{3}$ is equal to

$\begin{bmatrix} 8 & 0 \\ 0 & 8 \end{bmatrix}$

$\begin{bmatrix} 8 & 8 \\ 8 & 8 \end{bmatrix}$

$\begin{bmatrix} 6 & 0 \\ 0 & 6 \end{bmatrix}$

$\begin{bmatrix} 2 & 0 \\ 0 & 2 \end{bmatrix}$

If $A$ is a matrix of order $3\times 4$ and $B$ is a matrix of order $4\times 3$, then which of the following is true?

$AB$ is of order $3\times 3$ and $BA$ is of order $4\times 4$

$AB$ is of order $4\times 4$ and $BA$ is of order $3\times 3$

Neither $AB$ nor $BA$ is defined

Only $AB$ is defined and it is of order $3\times 3$

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Bihar Board Class 12 Science Mathematics · Ch 3: Matrices

Bihar Board Class 12 Science Mathematics · Ch 3: Matrices is an online chapter test in the Bihar Board Class 12 Science pattern, covering Matrices. Attempt it on SeatBeat with a timer like the real exam, then see a detailed solution for every question and your score and weak-topic analysis.

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Topics in this test

Topic	Subject	Questions
Matrices	Mathematics	30

Difficulty: 7 medium · 23 hard

Matrices MCQ questions with answers

The first 3 of 30 questions. Unlock the series for the rest, each with a solution.

Q1. If $A=\begin{bmatrix} 2 & 0 \\ 0 & 2 \end{bmatrix}$, then $A^{3}$ is equal to
यदि $A=\begin{bmatrix} 2 & 0 \\ 0 & 2 \end{bmatrix}$ हो, तो $A^{3}$ बराबर है
- A. $\begin{bmatrix} 8 & 8 \\ 8 & 8 \end{bmatrix}$
- B. $\begin{bmatrix} 6 & 0 \\ 0 & 6 \end{bmatrix}$
- C. $\begin{bmatrix} 2 & 0 \\ 0 & 2 \end{bmatrix}$
- D. $\begin{bmatrix} 8 & 0 \\ 0 & 8 \end{bmatrix}$
Solution
Here $A=2I$ is a scalar matrix, so $A^{3}=(2I)^{3}=8I=\begin{bmatrix} 8 & 0 \\ 0 & 8 \end{bmatrix}$.
यहाँ $A=2I$ एक अदिश आव्यूह है, अतः $A^{3}=(2I)^{3}=8I=\begin{bmatrix} 8 & 0 \\ 0 & 8 \end{bmatrix}$।
Q2. If $A$ is a matrix of order $3\times 4$ and $B$ is a matrix of order $4\times 3$, then which of the following is true?
यदि $A$ एक $3\times 4$ कोटि का आव्यूह है और $B$ एक $4\times 3$ कोटि का आव्यूह है, तो निम्नलिखित में से कौन-सा सत्य है?
- A. $AB$ is of order $3\times 3$ and $BA$ is of order $4\times 4$ / $AB$ की कोटि $3\times 3$ है और $BA$ की कोटि $4\times 4$ है
- B. $AB$ is of order $4\times 4$ and $BA$ is of order $3\times 3$ / $AB$ की कोटि $4\times 4$ है और $BA$ की कोटि $3\times 3$ है
- C. Neither $AB$ nor $BA$ is defined / न तो $AB$ और न ही $BA$ परिभाषित है
- D. Only $AB$ is defined and it is of order $3\times 3$ / केवल $AB$ परिभाषित है और इसकी कोटि $3\times 3$ है
Solution
Product is defined when the inner dimensions match: $AB$ is $3\times 3$ and $BA$ is $4\times 4$, and both products exist.
गुणनफल तब परिभाषित होता है जब भीतरी विमाएँ मेल खाती हों: $AB$ की कोटि $3\times 3$ और $BA$ की कोटि $4\times 4$ है, और दोनों गुणनफल अस्तित्व में हैं।
Q3. Consider the following statements about matrix multiplication (for matrices of suitable orders): (i) It is commutative. (ii) It is associative. (iii) It is distributive over addition. (iv) If $AB=O$, then $A=O$ or $B=O$. Which statements are correct?
आव्यूह गुणन के विषय में निम्नलिखित कथनों पर विचार कीजिए (उपयुक्त कोटियों के आव्यूहों के लिए): (i) यह क्रमविनिमेय है। (ii) यह साहचर्य है। (iii) यह योग पर वितरणात्मक है। (iv) यदि $AB=O$ हो, तो $A=O$ या $B=O$ होता है। कौन-से कथन सही हैं?
- A. (ii), (iii) and (iv) only / केवल (ii), (iii) और (iv)
- B. (ii) and (iii) only / केवल (ii) और (iii)
- C. (i) and (ii) only / केवल (i) और (ii)
- D. (i), (ii) and (iii) only / केवल (i), (ii) और (iii)
Solution
Matrix multiplication is associative and distributive over addition, but it is not commutative in general, and $AB=O$ does not force $A=O$ or $B=O$; so only (ii) and (iii) are correct.
आव्यूह गुणन साहचर्य तथा योग पर वितरणात्मक होता है, परंतु यह सामान्यतः क्रमविनिमेय नहीं होता, और $AB=O$ से यह आवश्यक नहीं कि $A=O$ या $B=O$ हो; अतः केवल (ii) और (iii) सही हैं।

Frequently asked questions

How many questions are in the Bihar Board Class 12 Science Mathematics · Ch 3: Matrices?

30 questions for 30 marks, to be answered in 20 minutes.

Is there negative marking in the Bihar Board Class 12 Science Mathematics · Ch 3: Matrices?

No — wrong answers are not penalised in this test.

Which topics does the Bihar Board Class 12 Science Mathematics · Ch 3: Matrices cover?

Matrices (30 questions).

Is the Bihar Board Class 12 Science Mathematics · Ch 3: Matrices free?

It is part of the BSEB Class 12 Science Test Series 2027 — Chapter-wise + Full Tests (41 tests, ₹149). You can first try Hindi · Ch 1: Chandradhar Sharma Guleri for free.

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