Mathematics Questions and Answers – Operations on Matrices


This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Operations on Matrices”.

1. The addition of matrices is only possible if they are of the same order.
a) True
b) False
View Answer

Answer: a
Explanation: The given statement is true. Addition of matrices is possible only if the matrices are of the same order. If there are two matrices of different order, then A+B is not defined.

2. If A = \(\begin{bmatrix}1&2&3\\9&10&11\end{bmatrix}\) and B = \(\begin{bmatrix}0&5&0\\5&0&5\end{bmatrix}\), then find A+B.
a) A+B = \(\begin{bmatrix}1&7&3\\11&10&16\end{bmatrix}\)
b) A+B = \(\begin{bmatrix}1&7&3\\14&11&13\end{bmatrix}\)
c) A+B = \(\begin{bmatrix}1&7&3\\14&10&16\end{bmatrix}\)
d) A+B = \(\begin{bmatrix}1&5&3\\14&10&16\end{bmatrix}\)
View Answer

Answer: c
Explanation: Given that, A = \(\begin{bmatrix}1&2&3\\9&10&11\end{bmatrix}\) and B = \(\begin{bmatrix}0&5&0\\5&0&5\end{bmatrix}\)
Then A+B = \(\begin{bmatrix}1+0&2+5&3+0\\9+5&10+0&11+5\end{bmatrix}\) = \(\begin{bmatrix}1&7&3\\14&10&16\end{bmatrix}\).

3. If A = \(\begin{bmatrix}3&4\\1&2\end{bmatrix}\) and B = \(\begin{bmatrix}1&5\\2&3\end{bmatrix}\), find 2A-3B.
a) \(\begin{bmatrix}3&7\\-4&5\end{bmatrix}\)
b) \(\begin{bmatrix}-3&-7\\-4&-5\end{bmatrix}\)
c) \(\begin{bmatrix}3&7\\-4&-5\end{bmatrix}\)
d) \(\begin{bmatrix}3&-7\\-4&-5\end{bmatrix}\)
View Answer

Answer: d
Explanation: Given that, A = \(\begin{bmatrix}3&4\\1&2\end{bmatrix}\) and B = \(\begin{bmatrix}1&5\\2&3\end{bmatrix}\)
⇒2A=2\(\begin{bmatrix}3&4\\1&2\end{bmatrix}\)=\(\begin{bmatrix}6&8\\2&4\end{bmatrix}\) and 3B=3\(\begin{bmatrix}1&5\\2&3\end{bmatrix}\)=\(\begin{bmatrix}3&15\\6&9\end{bmatrix}\)
∴2A-3B = \(\begin{bmatrix}6&8\\2&4\end{bmatrix}\)–\(\begin{bmatrix}3&15\\6&9\end{bmatrix}\)=\(\begin{bmatrix}3&-7\\-4&-5\end{bmatrix}\).

4. If A+B = \(\begin{bmatrix}6&7\\5&0\end{bmatrix}\)and A = \(\begin{bmatrix}2&5\\1&-1\end{bmatrix}\). Find the matrix B.
a) B = \(\begin{bmatrix}4&1\\2&4\end{bmatrix}\)
b) B = \(\begin{bmatrix}4&2\\4&1\end{bmatrix}\)
c) B = \(\begin{bmatrix}4&1\\4&2\end{bmatrix}\)
d) B = \(\begin{bmatrix}4&4\\4&2\end{bmatrix}\)
View Answer

Answer: b
Explanation: Given that, A+B = \(\begin{bmatrix}6&7\\5&0\end{bmatrix}\)and A = \(\begin{bmatrix}2&5\\1&-1\end{bmatrix}\)
⇒B=(A+B)-A = \(\begin{bmatrix}6&7\\5&0\end{bmatrix}\)–\(\begin{bmatrix}2&5\\1&-1\end{bmatrix}\)
B = \(\begin{bmatrix}4&2\\4&1\end{bmatrix}\)

5. Find the matrix M and N, if M+N = \(\begin{bmatrix}5&6\\7&8\end{bmatrix}\),M-N = \(\begin{bmatrix}4&5\\6&8\end{bmatrix}\).
a) M=1/2 \(\begin{bmatrix}9&11\\13&16\end{bmatrix}\), N=1/2 \(\begin{bmatrix}1&1\\1&0\end{bmatrix}\)
b) M=\(\begin{bmatrix}5&6\\7&8\end{bmatrix}\), N=\(\begin{bmatrix}4&5\\8&6\end{bmatrix}\)
c) M=1/2 \(\begin{bmatrix}9&2\\13&16\end{bmatrix}\), N=1/2 \(\begin{bmatrix}1&1\\2&5\end{bmatrix}\)
d) M=1/2 \(\begin{bmatrix}4&5\\1&2\end{bmatrix}\), N=1/2 \(\begin{bmatrix}1&2\\1&2\end{bmatrix}\)
View Answer

Answer: a
Explanation:M+N = \(\begin{bmatrix}5&6\\7&8\end{bmatrix}\)-(1) and M-N = \(\begin{bmatrix}4&5\\6&8\end{bmatrix}\)-(2)
Adding equation (1) and equation (2), (M+N)+(M-N)=2M=\(\begin{bmatrix}5&6\\7&8\end{bmatrix}\)+\(\begin{bmatrix}4&5\\6&8\end{bmatrix}\)
M=1/2 \(\begin{bmatrix}9&11\\13&16\end{bmatrix}\).
Subtracting equation (1) and equation (2), (M+N)-(M-N)=2N=\(\begin{bmatrix}5&6\\7&8\end{bmatrix}\)–\(\begin{bmatrix}4&5\\6&8\end{bmatrix}\)
N=1/2 \(\begin{bmatrix}1&1\\1&0\end{bmatrix}\).

6. Find the value of x and y if 2\(\begin{bmatrix}5&x\\y-4&6\end{bmatrix}\)+\(\begin{bmatrix}-4&1\\3&2\end{bmatrix}\)=\(\begin{bmatrix}6&3\\10&14\end{bmatrix}\)?
a) x=-1, y=9
b) x=-1, y=-9
c) x=1, y=-9
d) x=1, y=9
View Answer

Answer: d
Explanation: Given that, 2\(\begin{bmatrix}5&x\\y-4&6\end{bmatrix}\)+\(\begin{bmatrix}-4&1\\3&2\end{bmatrix}\)=\(\begin{bmatrix}6&3\\10&14\end{bmatrix}\)
Comparing the two matrices, 2x+1=3, 2y-8=10
Solving the two equations we get, x=1, y=9.

7. Find AB if A = \(\begin{bmatrix}1&2\\3&4\end{bmatrix}\) and B = \(\begin{bmatrix}1&5\\3&2\end{bmatrix}\).
a) AB = \(\begin{bmatrix}15&23\\9&7\end{bmatrix}\)
b) AB = \(\begin{bmatrix}9&7\\23&15\end{bmatrix}\)
c) AB = \(\begin{bmatrix}7&9\\15&23\end{bmatrix}\)
d) AB = \(\begin{bmatrix}7&9\\23&15\end{bmatrix}\)
View Answer

Answer: c
Explanation: Given that, A = \(\begin{bmatrix}1&2\\3&4\end{bmatrix}\) and B = \(\begin{bmatrix}1&5\\3&2\end{bmatrix}\)
Then, AB = \(\begin{bmatrix}1&2\\3&4\end{bmatrix}\)\(\begin{bmatrix}1&5\\3&2\end{bmatrix}\)

8. Matrix addition and matrix multiplication both are commutative.
a) True
b) False
View Answer

Answer: b
Explanation: The given statement is false. Matrix addition is commutative i.e. A+B=B+A. But matrix multiplication is not commutative i.e.AB≠BA.

9. Let A=\(\begin{bmatrix}3&-5&2\\-4&-6&2\\7&1&5\end{bmatrix}\). Find the additive inverse of A.
a) \(\begin{bmatrix}-3&5&-2\\-4&6&2\\7&1&5\end{bmatrix}\)
b) \(\begin{bmatrix}3&-5&2\\-4&-6&2\\7&1&5\end{bmatrix}\)
c) \(\begin{bmatrix}-3&5&-2\\4&6&-2\\-7&-1&-5\end{bmatrix}\)
d) \(\begin{bmatrix}-3&5&2\\-4&6&-2\\-7&-1&5\end{bmatrix}\)
View Answer

Answer: c
Explanation: Additive inverse of matrix A is the negative of A i.e. -A.
Therefore, -A=\(\begin{bmatrix}-3&5&-2\\4&6&-2\\-7&-1&-5\end{bmatrix}\)

10. Which of the following condition is incorrect for matrix multiplication?
a) A(BC)=(AB)C
b) A(B+C)=AB+AC
c) AB=0 if either A or B is 0
d) AB=BA
View Answer

Answer: d
Explanation: Matrix multiplication is never commutative i.e. AB≠BA. Therefore, the condition AB=BA is incorrect.

Sanfoundry Global Education & Learning Series – Mathematics – Class 12.

To practice all areas of Mathematics, here is complete set of 1000+ Multiple Choice Questions and Answers.

Participate in the Sanfoundry Certification contest to get free Certificate of Merit. Join our social networks below and stay updated with latest contests, videos, internships and jobs!

Manish Bhojasia - Founder & CTO at Sanfoundry
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter