TEST - 01
Topics : Algebra of Matrices
Max. Marks : 50
--------------------------------------------------------------------------------------------------------------------------- Select the correct option in the followings. Each question carries 1 mark.
Q01.
Let A  [a ij ]2 be a square matrix whose elements are given by a ij  (i)2  j . Then matrix A is
Q02.
 2 1
0 1
 0 3
1 0 
(b) 
(c) 
(d) 
(a) 




 3 0
 3 2
1 2
3 2 
7  2 7
x  y
If 
, then x.y 

x  y   9 4 
 9
(a) 0
(b) 1
(c) –3
(d) 3
2ix
2x
If a12  k sin x cos xe in a marix A   a ij  , where a ij  e sin jx , then value of k is
Q03.
Q04.
Q05.
23
(a) 1
(b) 1
(c) 2
If A and B are two matrices such that A  B is defined then
(a) A and B can be any matrices
(b) A and B are square matrices not necessarily of same order
(c) Number of columns in A  Number of rows in B
(d) A and B must be of same order
0 0 5
The matrix A   0 5 0  is a
 5 0 0 
(d) 2
(a) scalar matrix
(b) diagonal matrix (c) unit matrix
(d) square matrix
 2

x 
x
tan   
 cos2 (x) tan   
sin (x)

 

Q06. If A  
, then the value of A – B is
, B
 x



x
2
2
cot (x) 
 sin   cosec (x) 
 sin  
 
  



1
(a) I
(b) O
(c)
I
(d) 2 I
2
1 2
 2 3
Q07. If A  
, B

 and 4A  3B  C  O , then C is
3 4
 4 5
 2 1
2 1 
 2 1 
 2 1 
(a) 
(b) 
(c) 
(d) 




0 1 
 0 1
 0 1
 1 0 
Q08. If a matrix has 13 elements, then the possible dimensions it can have are
(a) 113, 13 1
(b) 1 26, 26 1
(c) 2 13, 13  2
(d) 1 13 only
Q09. If a matrix A has 12 elements then, how many different orders it can have?
(a) 112, 2  6, 3  4, 4  3, 6  2, 12 1
(b) 2  6, 3  4, 4  3, 6  2
(c) 6
(d) 112, 12 1
Q10. How many matrices of order 2  3 are possible with each entry 0 or 1?
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(a) 25
Q11.
5

Let A  0

0

(b) 128
0
25
x
0
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(c) 26
(d) 212
0

0  . If A is a scalar matrix, then value of x is

x 
(a) 5
Q12.
Q13.
(b) only 5
(c) only –5
(d) x can be any real number
 cos   sin  
If A  
 , then for what value of  is A an identity matrix?
 sin  cos  
n
, nZ
(a)   n, n  Z
(b)   3n, n  Z
(c)   2n, n  Z
(d)  
2
 x 2   x   2 
The values of x and y, if  2   3      , are
 y   2y   9 
(a) x  1, 2; y  3  3 2
Q14.
(c) x  1, 2; y  3 2  3
(d) x  1, 2; y  3  2 3
0 3 
 0 4a 
a
If A  
and kA  

 , then the value of (k) is
2

5

8
5b




(a) 64
Q15.
Q16.
Q17.
Q18.
Q19.
2
(b) x  1,  2; y  3  3 2
(b) 64
(c) 64
(d) 
1
64
3y   x  3 y 2  2 
 2x  y
The values of x and y, if 

 are
y 2  5y   0
6 
 0
(a) x  1, y  1, 2
(b) y  1, x  2
(c) x  1, y  1
(d) x  1, y  2
0
y x
 1


0
0  is a diagonal matrix?
For what value (s) of x, the matrix  0
 0 x  y6
5 

(a) 6
(b) 0
(c) 3
(d) 2
 1 2 1 
If A   3 4 7  , then the value of X where A  X is a unit matrix, is
5 1 6 


 0 2 1 
 0 3 5 
 0 1 2 
0 0 0








(a)  3 3 7  (b)  2 3 1 
(c)  3 3 7 
(d)  0 0 0 
 5 1 5 
 1 7 6 
5 1 6 
0 0 0








4 0 0


If  0 4 0  is a scalar matrix, then the value of x y is
y 0 x


(a) 4
(b) 0
(c) 1
(d) 4
5 0 0 


For what value of m, the matrix  0 5 0  is a diagonal matrix?
3 0 m


(a) any real no.
(b) 0
(c) 5
(d) no value of m
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Q20.
Q21.
1 9 3 
For the matrix 
 , no. of rows and columns are denoted by ‘m’ and ‘n’ respectively.
 0 4 1
Then value of (m  n) m 
(a) 3
(b) 2
(c) 5
(d) 25
4 7 5 


Let A   3 6 1 and a ij denote the elements of A. Then a12  a 31  a 21 
8 0 2 


(a) 10
Q22.
Q23.
Q24.
Q25.
Q26.
Q27.
Q28.
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(b) 2
(c) 8
 1 0 0


Let A   x y 0  be a unit matrix of order 3. Then x  y 
 0 0 1


(a) 0
(b) 2
(c) 1
5 1
 1 2 
If 3A  B  
, A

 , then matrix B is given by
3 4
 6 0
 8 5 
 8 15 
 8 5 
(a) 
(b) 
(c) 



 15 4 
 5 4 
 15 4 
1 0 
 1 1 
If A  B  
and A  2B  

 , then A 
1 1 
 0 1
1/3 1/3
1/3 2/3
1/3 2/3
(a) 
(b) 
(c) 



 2/3 1/3
 2/3 1/3 
1/3 1/3 
If A  diag. 1 2  , B  diag.  3 6  , then 3A  B 
(d) 4
(d) 1
 8 15 
(d) 

 5 4 
(d) None of these
(b) diag.  0 6 
(c) diag.  6 6 
(d) diag.  6 6 
(a) diag.  6 0 
Which of the following is ‘additive identity for matrix addition’?
(a) any matrix
(b) any square matrix
(c) any null matrix
(d) a null matrix of same order
A null matrix, whose all elements are zero, is
(a) always a square matrix
(b) always a column vector
(c) always a diagonal matrix
(d) not necessary to be a square matrix
8 
6
P

For the matrix P   4 10  ,  is given by
2
 2 24 
3 4
(a)  2 5


 1 12 
Q29.
Q30.
 3 4 
 3 4 
3 4




(b) 2 5
(c) 2 5
(d)  2 5 






 1 12 
 1 12 
 1 12
m a t h 
Order of the matrix  m i s s  is
 i o n 12 
(a) 4  3
(b) 3  4
(c) 3/4
(d) 4/3
How many non-diagonal matrices of order 3 can be formed with each entry 0 or 1?
(a) 512
(b) 1024
(c) 504
(d) 8
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Q31.
Q32.
7 
 5 6

2
If  6 2 m  6  is a symmetric matrix, then m 
 7 3
0 
(a) 0
(b) 2
(c) 2
2
Let A  (a ij ) mm . If A  A , then 7A  (I  A)3 
(a)  I
Q33.
Q34.
Q35.
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(b) I
(c) 2I
(d) 3
(d) O
1 2 2
If A   2 1 2  satisfies A A T  9 I , then the value of x will be
 2 x 1
(a) 2
(b) 2
(c) 0
(d) 1
 13 
 
Let A   0 71 29   12  . Then order of matrix A 
 31
 
(a) 3  3
(b) 1 3
(c) 1 1
(d) 3  1
 1 0  7 
In the product 
  , the pre-factor matrix is
 5 7  2 
7
(a)  
 2
Q36.
Q37.
Q38.
Q39.
Q40.
Q41.
4
 7
1 0
 1 0
(b) 
(c) 
(d) 



 21
0 1
 5 7 
 2 3
 1 2 3 


Let A  
 and B   4 5  . If BA  (bij ) , then value of b 21 

4
2
4


 9 8 


(a) 16
(b) 16
(c) 36
(d) 0
 2 1
 1 8 

 m n  

If  1 0  
   1 2  , then the value of (m  n  x  y) is
 3 4   x y   9 22 




(a) 8
(b) 6
(c) 10
(d) 6
0
2


If A  
, then A 4 

 2 0
(a) O
(b) 4 I
(c) 16 I
(d) I
T
If order of A is 3  5 , then order of matrix A is
(a) 3  5
(b) 3  3
(c) 5  5
(d) 5  3
 cos  sin  

Let A  
; 0    . If A satisfies A  A  2 I , then 4 

2
  sin  cos  



(a) 
(b)
(c)
(d)
4
2
6
 16 574 875 
If 574 97 37   P  Q , where P is symmetric and Q is skew symmetric matrix, then Q 


875 37 709
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Q42.
Q43.
Q44.
Q45.
Q46.
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574 875
 0
0 0 0


0
37 
(a)  574
(b)  0 0 0 
 875 37
 0 0 0 
0 
 16 574 875 
 16 574 875 


37
(c)  574 97
(d) 574 97 37 

 875 37 709 
875 37 709 
 2 1
2
Matrix A  
 satisfies 4 A  A  k I . Then k 

1
2


(a) 3
(b) 1
(c) 3
(d) 0
1 3
 2 3 
If A  
and B  

 such that AB  2 I , then inverse of matrix A is
0 2
0 1 
 2 3 
1 3
1 1 3
1  2 3 
(a) 
(b) 
(c) 
(d) 




2 0 2
2 0 1 
0 1 
0 2
If A and B are invertible matrices of the same order; such that (BA) 1  A 1B k , then k equals
(a) 1
(b) 1
(c) 0
(d) no value of k is possible
2 3 
be such that A 1  m A , then the value of m is
If A  

 5 2 
1
1
(a) 19
(b)
(c) 
(d) 19
19
19
 2 1
2
If A  
 and A   A   I  O , then the value of    

1
2


(a) 7
(b) 1
(c) 1
(d) 7
Question numbers 47 to 50 are Assertion and Reason based questions. Two statements are given,
one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the
codes (a), (b), (c) and (d) as given below.
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true.
Q47.
 1 1
 1 7 4
, then P   7 2  .
Assertion (A) : If P  



 1 2 6 
 4 6 
Reason (R) : If P and Q are matrices of order m  n and n  y respectively, then the order of
matrix PQ is m  y .
Q48.
Q49.
 0 1 1 
Assertion (A) : The matrix given by M   1 0 5 is a symmetric matrix.
 1 5 0 
Reason (R) : If P and Q are square matrices of same order such that PQ  QP  I , then we
always have P 1  Q and Q 1  P .
 1 3 4 
 1 3 4 
Assertion (A) : If X  
, then X  

.
 0 2 5
0 2 5 
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Reason (R) : An element present in the i th row and jth column in the matrix B   bij 
is
m n
given by bij .
Q50.
0 0 0
Assertion (A) : Matrix M   0 0 0  is a diagonal matrix.
 0 0 0 
Reason (R) : The diagonal matrix is a square matrix, in which all the non-diagonal elements are
zero.
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