Mathematics

Multiple Choice Questions (MCQ)
MCQ | Class 12 | Chapter 3
MATRICES

MCQ Based on the different types of Matrices
MCQ Based on the Addition, Subtraction and Multiplication of Matrices.
MCQ Based on the Transpose, Symmetric and Skew Symmetric of Matrices
MCQ Based on the general problems of Matrices.

Features

In this pdf given below you find the important MCQ which are strictly according to the CBSE syllabus and are very useful for the CBSE Examinations.
Solution Hints are also given to some difficult problems.
Each MCQ contains four options from which one option is correct.
On the right hand side column of the pdf Answer option is given.

Action Plan

First of all students should Learn and write all basic points and Formulas related to the Matrices.
Start solving the NCERT Problems with examples.
Solve the important assignments on the Matrices.
Then start solving the following MCQ.

MCQ | CHAPTER 3 | CLASS 12

MATRICES

Question 1

If A
and B are symmetric matrices of the same order, then

a) AB is a symmetric matrix

b) A
– B is a skew-symmetric matrix

c) AB + BA is a symmetric matrix

d) AB
– BA is a symmetric matrix

Answer: c

Question 2

If a matrix A is
symmetric as well as skew symmetric then

a) A is a diagonal
matrix

b) A is a null matrix

c) A is a unit matrix

d) A is a triangular
matrix

Answer: b

Question 3

If A = $\begin{bmatrix}3 & x-1 \\2x+3 & x+2 \\\end{bmatrix}$ is a symmetric matrix, then x =

a) 4

b) 3

c)
-4

d) -3

Answer: c

Question 4

If A is a square matrix,
then A – A’ is a

a)
diagonal matrix

b) skew-symmetric
matrix

c)
symmetric matrix

d) none of these

Answer: b

Question 5

If A
is any square matrix, then which of the following is skew – symmetric?
a) A + A^T

b) A
– A^T

c) AA^T

d) A^TA

Answer: b

Question 6

If A = $\begin{bmatrix}4 & 2 \\-1 & 1 \\\end{bmatrix}$ then
(A – 2I)(A – 3I) =

a) A

b)
I

c)
O

d)
5I

Answer
c

Question 7

If A = $\begin{bmatrix}a & b \\b & a \\\end{bmatrix}$ and A²
= $\begin{bmatrix}\alpha & \beta \\\beta & \alpha \\\end{bmatrix}$ , then

a) α = a² +
b², β = ab

b) α = a² +
b², β = 2ab
c) α = a² + b², β = a² – b²

d) α = 2ab, β = a² +
b²

Answer b

Question 8

If A = $\begin{bmatrix}1 & 2 & x \\0 & 1 & 0 \\0 & 0 & 1 \\\end{bmatrix}$ and B = $\begin{bmatrix}1 & -2 & y \\0 & 1 & 0 \\0 & 0 & 1 \\\end{bmatrix}$ and AB
= I₃, then x + y equals

a) 0

b) -1

c) 2

d) None of these

Answer a

Question 9

If A = $\begin{bmatrix}1 & 2 \\2 & 1 \\\end{bmatrix}$ and f(x) = (1 + x)(1 – x), then f(A) is

$a)\; -4\begin{bmatrix}1 & 1 \\1 & 1 \\\end{bmatrix}$

$b)\; -8\begin{bmatrix}1 & 1 \\1 & 1 \\\end{bmatrix}$

$c)\; 4\begin{bmatrix}1 & 1 \\1 & 1 \\\end{bmatrix}$

$d)\; -14\begin{bmatrix}1 & 1 \\1 & 1 \\\end{bmatrix}$

Answer: a

Question: 10

Total number of
possible matrices of order 2 X 3 with each entry 1 or 0 is

a) 6

b) 36

c) 32

d) 64

Answer: d

Question 11

If A = $\begin{bmatrix}1 & 3 \\3 & 4 \\\end{bmatrix}$ and A² – KA – 5I = 0, then k =

a)
5

b) 3

c) 7

d) None
of these

Answer: a

Question 12

$\begin{bmatrix}7 & 1 & 2 \\9 & 2 & 1 \\\end{bmatrix}\begin{bmatrix}3 \\4 \\5\end{bmatrix}+2\begin{bmatrix} 4\\2\end{bmatrix}$ is equal to

$a)\; \begin{bmatrix}43 \\44\end{bmatrix}$

$b)\; \begin{bmatrix}45 \\44\end{bmatrix}$

$c)\; \begin{bmatrix}43 \\45\end{bmatrix}$

$d)\; \begin{bmatrix}47 \\45\end{bmatrix}$

Answer a

Question 13

If A = $\begin{bmatrix}1 & -2 & 1 \\2 & 1 & 3 \\\end{bmatrix}$ and B
= $\begin{bmatrix}2 & 1 \\3 & 2 \\1 & 1 \\\end{bmatrix}$ , then
(AB)^T is equal to

$a)\; \begin{bmatrix}-3 & -2 \\10 & 7 \\\end{bmatrix}$

$b)\; \begin{bmatrix}-3 & 10 \\-2 & 7 \\\end{bmatrix}$

$c)\; \begin{bmatrix}3 & 2 \\10 & 7 \\\end{bmatrix}$

$d)\; \begin{bmatrix}-3 & 2 \\10 & 17 \\\end{bmatrix}$

Answer b

Question 14

If matrix A = $\begin{bmatrix}a & b & c \\b & c & a \\c & a & b \\\end{bmatrix}$

where a, b, c are real
positive numbers, abc = 1 and A^TA = I,

then the value of a³ +
b³ + c³ is

a) 1

b) 2

c) 3

d) 4

Answer d

Solution Hint: A’A = I ⇒ A² = I

Comparing these two matrices we get

a² + b² + c² =
1,

ab + bc + ca = 0,

ac + ba + bc = 0,

bc + ac + ab = 0

Now using
(a + b + c)² and find the value of (a + b + c) we get (a + b
+ c) = 1

Using identity: a³+ b³+ c³
– 3abc find the value of a³ +
b³ + c³

Question 15

The
order of the matrix A is 3 x 5 and that
of matrix B is 2 x 3. Then order of the
matrix BA is

a) 2 x 3

b) 3 x
2

c) 2 x
5

d) 5 x
2

Answer: c

Question 16

If a matrix A is
both symmetric and skew symmetric then
matrix A is

a) a scalar matrix

b) a diagonal matrix

c) a zero matrix of
order n x n

d) a rectangular
matrix.

Answer; c

Question: 17

If A = $\begin{bmatrix}1 & -3 \\2 & k \\\end{bmatrix}$ and A²
– 4A + 10 I = A, then k =

a)
– 4

b)
0

c)
1 or 4

d)
4 and not 1

Answer:
d

Question:18

$\begin{bmatrix}1 & x & 1 \\\end{bmatrix}\begin{bmatrix}1 & 3 & 2 \\2 & 5 & 1 \\15 & 3 & 2 \\\end{bmatrix}\begin{bmatrix} 1\\2 \\x\end{bmatrix}=O$ if the value of x is

a) – 7

b) – 11

c) – 2

d) 14

Answer: c

Question:19

If A = $\begin{bmatrix}2x & 0 \\x & x \\\end{bmatrix}$ and A^-1
= $\begin{bmatrix}1 & 0 \\-1 & 2 \\\end{bmatrix}$ , then x equals

a) 2

b) -1/2

c) 1

d) 1/2

Answer: d

Question:20

For any square matrix A,
AA^T is a
a) unit
matrix

b) symmetric matrix

c)
skew-symmetric matrix

d) diagonal matrix

Answer: b

Question:21

If the matrix A = $\begin{bmatrix}5 & 2 & x \\y & 2 & -3 \\4 & t & -7 \\\end{bmatrix}$ is a symmetric matrix, then find the value of
x, y and t respectively

a) 4, 2, 3

b) 4, 2, -3

c) 4, 2, -7

d) 2, 4, -7

Answer: b

Question:22

If a matrix A is both
symmetric and skew-symmetric, then

a) A is a
diagonal matrix

b) A is a zero matrix

c) A is a
scalar matrix

d) A is a square matrix

Answer: b

Question:23

The matrix A = $\begin{bmatrix}0 & 1 \\1 & 0 \\\end{bmatrix}$ is a

a) unit matrix

b) diagonal matrix

c) symmetric matrix

d) skew-symmetric
matrix

Answer: d

Question: 24

If A² –
A + I = O, then the inverse of A is
a) I – A

b) A
– I

c) A

d) A
+ I

Answer: a

Question: 25

If $\begin{bmatrix}x-y-z \\-y+z \\z\end{bmatrix}=\begin{bmatrix}0 \\5 \\3\end{bmatrix}$ then the value of x, y, z are respectively

a) 5, 2, 2

b) 1, -2, 3

c) 0, -3, 3

d) 11, 8, 3

Answer: b

Question: 26

Total
number of possible matrices of order 3 × 3 with each entry 2 or 0 is
a) 9

b) 27

c) 81

d)
512

Answer: d

Question: 27

The matrix $\begin{bmatrix}0 & -5 & 8 \\5 & 0 & 12 \\-8 & -12 & 0 \\\end{bmatrix}$ is a

a)
diagonal matrix

b) symmetric matrix

c) skew symmetric
matrix

d) scalar matrix

Answer: c

Question: 28

If A
is a matrix of order m × n and B is a matrix such that AB’ and B’A are both
defined, then the order of matrix B is
a) m × m

b) n
× n

c) n
× m

d) m
× n

Answer: d

Question: 29

If A
and B are matrices of the same order, then (AB’ – BA’) is a
a) skew-symmetric matrix

b)
null matrix

c)
symmetric matrix

d)
unit matrix

Answer a

Question: 30

If A is a square matrix
such that A² = I, then (A – I)³ + (A + I)³ –
7A is equal to
a) A

b) I – A

c) I + A

d) 3A

Answer: a

Question: 31

If A² = A,
then (I + A)⁴ is equal to

a) I + A

b) I + 4A

c) I + 15 A

d) None of these

Answer: c

Question: 32

If A is an m × n matrix
such that AB and BA are both defined, then B is a
a) m × n
matrix

b) n × m matrix

c) n × n matrix

d) m × n matrix

Answer: b

Question: 33

Which
of the given values of x and y make the following pairs of matrices equal

$\begin{bmatrix}3x+7 & 5 \\y+1 & 2-3x \\\end{bmatrix},\; \begin{bmatrix}0 & y-2 \\8 & 4 \\\end{bmatrix}$

a) x = -1/ 3, y = 7

b) Not possible to find

c) y = 7,
x = -2/ 3

d) x = -1/ 3, y = -2/ 3

Answer: b

Question 34

If A
is a symmetric matrix then, then A² is a

a) symmetric matrix

b)
Identity matrix

c)
skew symmetric matrix

d)
null matrix

Answer: a

Question: 35

Suppose
P and Q are two different matrices of order
3 x n and n x p, then the order of the matrix P x Q is
?

a) 3 x p

b) p x
3

c) n x n

d) 3 x 3

Answer: a

Question: 36

Find the order of the following

$\begin{bmatrix}1 & -1 \\0 & 2 \\2 & 3 \\\end{bmatrix}\left\{ \left [ \begin{matrix}-1 & 0 & 2 \\2 & 0 & 1 \\\end{matrix} \right ]-\begin{bmatrix}0 & 1 & 23 \\1 & 0 & 21 \\\end{bmatrix}\right\}$

a) 2 x 3

b)
2 x 2

c) 3 x 2

d)
3 x 3

Answer: d

Question: 37

Matrices A and
B will be inverse of each other only if

a) AB = BA

b) AB = BA = 0

c) AB = 0, BA = 1

d) AB
= BA = I

Answer: d

Question: 38

Total number of
possible matrices of order 2 X 3 with each entry 1 or 0 is

a) 6

b) 36

c) 32

d) 64

Answer: d

Question: 39

If a matrix A is
both symmetric and skew symmetric then
matrix A is

a) a scalar matrix

b) a diagonal matrix

c) a zero matrix of
order n x n

d) a rectangular
matrix.

Answer: c

Question: 40

$If\: A=\begin{bmatrix}2 & -3 & 4 \\\end{bmatrix},B=\begin{bmatrix}3 \\2 \\2\end{bmatrix},X=\begin{bmatrix}1 & 2 & 3 \\\end{bmatrix},Y=\begin{bmatrix}2 \\3 \\4\end{bmatrix}$

Then find AB + XY

a) [28]

b) [24]

c) [32]

d) None of these

Answer: a

Question: 41

If A = $\begin{bmatrix}1 & 1 \\1 & 1 \\\end{bmatrix}$ then A¹⁰⁰ is equal to

a)
2¹⁰⁰A

b) 2⁹⁹ A

c)
100A

d)
299 A

Answer:
b

Solution Hint

We have, A = $\begin{bmatrix}1 & 1 \\1 & 1 \\\end{bmatrix}$

A² = A x A = $\begin{bmatrix}2 & 2 \\2 & 2 \\\end{bmatrix}$ = 2 $\begin{bmatrix}1 & 1 \\1 & 1 \\\end{bmatrix}$ = 2A

A⁴ = A² . A² = 2A . 2A = 4 A²
= 4 x 2A = 8A = 2³A

Similarly A⁸ = 2⁷A ⇒ A¹⁰⁰ = 2⁹⁹ A

Question: 42

The
matrix $\begin{bmatrix}1 & 0 & 0 \\0 & 2 & 0 \\0 & 0 & 4 \\\end{bmatrix}$ is a

a)
Identity Matrix

b)
Symmetric Matrix

c)
Skew – Symmetric Matrix

d) None of these

Answer: b

Question: 43

Each
diagonal element of a skew symmetric matrix is

a)
zero

b)
positive

c)
non-real

d)
negative

Answer: a

Question: 44

If A
and B are symmetric matrix of same order, then
AB – BA is a :

a)
Skew – Symmetric Matrix

b) Symmetric
Matrix

c)
Zero Matrix

d)
Identity Matrix

Answer: a

Question: 45

If A
is a square matrix such that A²
= I, then (A – I)³ + (A + I)³
– 7A is equal to

a)
A

b) I –
A

c) I + A

d) 3 A

Answer a

Question: 46

$If\; \begin{bmatrix}1 & x & 1 \\\end{bmatrix}\begin{bmatrix}1 & 3 & 2 \\0 & 5 & 1 \\0 & 2 & 0 \\\end{bmatrix}\begin{bmatrix}1 \\1 \\x\end{bmatrix}=O$

Then
the values of x are

a) 1, 5

b) -1,
-5

c) 1,6

d) -1,
-6

Answer: d

Question 47

If A = $\begin{bmatrix}-3 & 5 & -8 \\x & 5 & 5 \\0 & y & 4 \\\end{bmatrix}$ is upper triangular matrix, then x + y is

a)
3

b)
-3

c) 0

d) 1

Answer: c

Question 48

Sum of
two symmetric matrix is always

a) symmetric matrix

b)
Identity matrix

c)
skew symmetric matrix

d)
None of these

Answer c

Question 49

Which
of the following matrices both symmetric
and skew symmetric matrix ?

a) Identity matrix

b) Unit matrix

c)
Null matrix

d)
None of these

Answer: c

Question 50

If A = $\begin{bmatrix}x & 0 \\1 & 1 \\\end{bmatrix}$ and B
= $\begin{bmatrix}1 & 0 \\5 & 1 \\\end{bmatrix}$ ,
then find the value of x for which A²
= B

a)
1

b) -1

c)
4

d)
None of these

Answer: d

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Maths MCQ Class 12 Ch- 3 | Matrices

Mathematics

Multiple Choice Questions (MCQ)
MCQ | Class 12 | Chapter 3
MATRICES

Features

Action Plan

MCQ | CHAPTER 3 | CLASS 12

MATRICES

Leave a Comment Cancel reply

Mathematics

Multiple Choice Questions (MCQ)MCQ | Class 12 | Chapter 3MATRICES

Features

Action Plan

MCQ | CHAPTER 3 | CLASS 12

MATRICES

Leave a Comment Cancel reply

Multiple Choice Questions (MCQ)
MCQ | Class 12 | Chapter 3
MATRICES