The pdf contains multiple type questions on the topic MATRICES.
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CHAPTER 3
MATRICES
MULTIPLE CHOICE TYPE QUESTIONS
1. 𝐼𝑓 𝐴 = (𝑎𝑖𝑗 )𝑚×𝑛 𝑖𝑠 𝑎 𝑠𝑐𝑎𝑙𝑎𝑟 𝑚𝑎𝑡𝑟𝑖𝑥, 𝑖𝑓
A) 𝑎𝑖𝑗 = 0, 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑖 ≠ 𝑗
B) 𝑎𝑖𝑗 = 𝑠𝑜𝑚𝑒 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑘, 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑖 = 𝑗 𝑎𝑛𝑑 𝑎𝑖𝑗 = 0, 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑖 ≠ 𝑗
C) 𝑎𝑖𝑗 = 0, 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑖 = 𝑗
D) 𝑎𝑖𝑗 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡, 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑖 = 𝑗 𝑎𝑛𝑑 𝑎𝑖𝑗 = 0, 𝑓𝑜𝑟 𝑠𝑜𝑚𝑒 𝑖 ≠ 𝑗
(𝑖−𝑗)2
2. 𝐼𝑓 𝐴 = (𝑎𝑖𝑗 )𝑚×𝑛 𝑤𝑖𝑡ℎ 𝑎𝑖𝑗 = 𝑡ℎ𝑒𝑛 𝐴 =
2
0 1/2 0 −1/2 1/2 0 −1/2 0
𝐴) ( ) B) ( ) C) ( ) D) ( )
1/2 0 −1/2 0 0 1/2 0 −1/2
3. 𝐼𝑓 𝐴 𝑎𝑛𝑑 𝐵 𝑎𝑟𝑒 𝑚𝑎𝑡𝑟𝑖𝑐𝑒𝑠 𝑤𝑖𝑡ℎ 𝐴𝐵 = 0 𝑎𝑛𝑑 𝐵𝐴 = 0, 𝑡ℎ𝑒𝑛
A) 𝐴 = 0 𝑜𝑟 𝐵 = 0 B) 𝑒𝑖𝑡ℎ𝑒𝑟 𝐴 = 0 𝑜𝑟 𝐵 = 0
C) 𝐴 = 0 𝑎𝑛𝑑 𝐵 = 0 D) None
𝑐𝑜𝑠𝑥 −𝑠𝑖𝑛𝑥 0
4. 𝐼𝑓 𝐴(𝑥) = ( 𝑠𝑖𝑛𝑥 𝑐𝑜𝑠𝑥 0) , 𝑡ℎ𝑒𝑛 𝐴(𝑥). 𝐴(𝑦) =
0 0 1
𝐴) 𝐴(𝑥. 𝑦) B) A(x+y) C) A(x-y) D) None
5. The principal diagonal elements of a skew symmetric matrix are
A) 1 B) 0 C) 0 or 1 D) None
𝑎 ℎ 𝑔 𝑥
6. What is the order of the matrix (𝑥 𝑦 𝑧) (ℎ 𝑏 𝑓 ) (𝑦)
𝑔 𝑓 𝑐 𝑧
A) 3x1 B) 1x1 C) 1x3 D) 3x3
7. The number of all possible matrices of order 3x3 with each entry 0 or 1 is:
A) 27 B) 81 C) 18 D) 512
2 3
2 1 3
8. 𝐼𝑓 𝐴 = ( ) 𝑎𝑛𝑑 𝐵 = (4 2) , 𝑡ℎ𝑒𝑛
4 5 6
1 5
A) Only AB is defined B) Only BA defined
C) AB and BA both are defined D) AB and BA both are not defined
0 −2 4
9. The matrix ( 2 0 6) 𝑖𝑠
−4 −6 0
A) Diagonal matrix B) Symmetric matrix
C) Skew symmetric matrix D) Scalar matrix
1 2
10. 𝐼𝑓 𝐴 = ( ) 𝑎𝑛𝑑 𝐴2 − 𝑘𝐴 − 𝐼2 = 0, 𝑡ℎ𝑒𝑛 𝑘 =
2 3
𝐴) 4 B) -4 C) 8 D) -8
11. If A is a 2x3 matrix and AB is 2x5 matrix, then B must be a
A) 3x5 matrix B) 5x3 matrix C) 3x2 matrix D) 5x2 matrix
16.Choose the correct option
(A) Every scalar matrix is an identity matrix
(B) Every square matrix whose each element is 1 is an identity matrix
(C) Every scalar matrix is a diagonal matrix
(D) Every diagonal matrix is a scalar matrix
17.Assume X, Y, Z, W and P are matrices of order 2 × n, 3 × k, 2 × p, n × 3 and p × k,
Respectively. The restriction on n, k and p so that PY + WY will be defined are
(A)k = 3, p = n
(B) k is arbitrary, p = 2
(C) p is arbitrary, k = 3
(D) k = 2, p = 3
18.The number of all possible matrices of order 2 × 3 with each entry 3 or 4.
(A) 24
(B) 20
(C) 64
(D) 36
19. Order of matrices A, B and C are 2 × 3, 3 × 4 𝑎𝑛𝑑 4 × 4 respectively then the order of matrix
(AB)C is
(A)2 × 4
(B)3 × 3
(C)2 × 3
(D)3 × 4
20. If a matrix is symmetric as well as skew-symmetric then it must be a
(A) Square matrix
(B) Diagonal matrix
(C) Null matrix
ZIET, BHUBANESWAR Page 2
, (D) Identity matrix
6 𝑥+5
21. If matrix [ ] is symmetric, then value of x is
2𝑥 + 3 3𝑥 + 3
(A) 3
(B) 2
(C) 4
(D) x may take any real value
22. If A is square matrix, then A - 𝐴𝑇 is
(A) Null matrix
(B) Square matrix
(C) Symmetric matrix
(D) Skew symmetric matrix
5 0 0
23. The matrix[0 5 0]is
0 0 5
(A) Square matrix
(B) Diagonal matrix
(C) Scalar matrix
(D) All of these
1 0 0
24. If A=[0 1 0], then 𝐴𝑛 𝑖𝑠 𝑒𝑞𝑢𝑎𝑙𝑠 𝑡𝑜
0 0 1
𝑛 0 0
(A)[0 𝑛 0]
0 0 𝑛
1 0 0
(B)[0 1 0]
0 0 1
0 0 0
(C)[0 0 0]
0 0 0
(D)None of these
𝑐𝑜𝑠𝑥 −𝑠𝑖𝑛𝑥
25. If A = [ ] and A + AT = I, then value of x is
𝑠𝑖𝑛𝑥 𝑐𝑜𝑠𝑥
(A) π/6
(B) π/3
(C) 2π
(D) 3π/2
ZIET, BHUBANESWAR Page 3
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