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Mathematics Matrices and Determinants Online Test

Mustansar KhanLast Updated: October 15, 2025

Important Math Matrices and Determinants Question and Answer

Total Questions:	82
Time Allowed:	40 Minutes
Total Marks:	82
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Math Matrices and Determinants Practice Test Online With Explanation

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Page 1 of 4

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1. The transpose of a row matrix is a

Column matrix

Scalar matrix

Diagonal matrix

Zero matrix

2. If a is matrix of order m x n and B is a matrix of order n x p then order of AB is

p x n

p x p

n x p

m x p

4. Let A be a square matrix. Then, ½ (A – A) is

Null

Symmetric

None of the above

Skew-symmetric

Diagonal matrix

Scalar matrix

Zero matrix

Column matrix

6. If A = [aij] is (m x n) matrix, then transpose of A is of the order.

m x m

m x n

n x n

n x m

Scairar matrix

Identity matrix

Odd matrix

Even matrix

8. If A is null matrix, then A/|A| is

∞

9. [0 0 0] is

Identity matrix

Null matrix

Scalar matrix

Diagonal matrix

10. Matrices A = [aij] 2 x 3 and B = [bij] 3 x 2 are suitable for

B²

A²

11. A and B be two square matrices and if their inverse exist, the (AB)¯¹ =

A¯¹B

A¯¹B¯¹

B¯¹A¯¹

AB¯¹

12. The additive inverse of a matrix A is

A²

Adj A/|A|

-A

13.

Zero matrix

Row matrix

Non – diagonal matrix

Identity matrix

14. An equation of the form ax + by = k is homogeneous linear equation when:

a ≠ 0, b ≠ 0, k = 0

a = -0, a ≠ 0

a = 0, b ≠ 0

b = 0, a = 0

15. A matrix having m rows and n columns with m ≠ n is said to be a

Square matrix

Rectangular matrix

Identity matrix

Scalar matrix

16. If |A| = 0, then A is

Non- singular matrix

Singular matrix

Zero matrix

17. The square matrix A is skew Hermitian when (Ā)ᵗ =

-A

Aᵗ

18. A matrix A over the filed C in which (A)ᵗ is called

Scalar matrix

Symmetric

Identity

Hermitian matrix

19. If A is a skew-symmetric matrix of order n and P, any square matrix of order n, prove that P’ AP is

Symmetric

Null

Skew-symmetric

Diagonal

20. For a square matrix A, if A = Aᵗ, then A is called:

Non-symmetric

Transpose

Symmetric

Matrix

21. A square matrix A = [aij] is lower triangular matrix when:

Cij = 0

Bij = 0

Dij = 0

Aij = 0 for all i < j

22.

None of these

-6

-4

23. (AB)t = ?

BᵗAᵗ

AᵗBᵗ

24.

a = 2, b = 2

a = 3, b = 3

a = 3, b = 2

a = 2, b = 3

25. [-1, 4 7 2] is a

Diagonal matrix

Column matrix

Row matrix

Scalar matrix

Page 2 of 4

26. If for the matrix A, A⁵ = I, then A¯¹ =

A²

A³

None of these

27. If A is non – singular matrix then (A¯¹)¯¹ = ?

Aᵗ

-A

28.

29. Let A = [aiJ]mxn I aj = 0 ∀i ≠ j and aj ≠ 0 for some 1 = j then matrix A is

None of these

Hermition matrix

Symmetric matrix

Diagonal matrix

30. If order of matrix A is 1 x 3 then orders of Aᵗ is

3 x 3

1 x 3

1 x 1

3 x 1

31.

-1

32.

3 x 1

3 x 2

2 x 3

2 x 2

33.

b³

b²

34. Trival solution of homogeneous linear equation is:

(1, 3, 5)

(1, 1, 1)

a, b and c

(1, 2, 3)

35. (ABC)’ =

CBA’

C’B’A’

C’B’A

CBA

36. Minimum number of equation for any system of equations

|A|= 0

|A| = ∞

|A| ≠ 0

None of these

37.

2 x 3

2 x 2

3 x 2

3 x 3

38. The leading diagonal or main diagonal of a square matrix known as

Both a and b

None of these

The secondary diagonal

The principal diagonal

39. If A is skew symmetric matrix, then Aᵗ =

-A

Diagonal matrix

40. Equation having a common solution are called

Homogeneous equations

Simultaneous equation

None of these

Linear equations

41. For trival solution |A| is:

|A|≠ 0

|A| = 0

A = 0

42.

Identity matrix

None of these

Diagonal matrix

Scalar matrix

43. Two matrices A and B are equal if

Number of columns of a is equal to number of rows of B

Both have same order

Both have same order and equal corresponding elements

Both are rectangular

44. Matrix obtained by interchanging its rows and columns is called

None of these

Symmetric

Transpose

Inverse

45. If the trace of a matrix A is 5, then the trace of the matrix 3A is

5/3

3/5

46. If A, B, and C are three matrices such that AB = C then which one is true?’ I = C/A, II = CA¯¹, III = A¯¹C

I and III

II and III

I only

III only

47. If A and B are matrices, then which from the following is true?

A + B ≠ B + A

(A¹) ≠ A

All are true

AB ≠ BA

48. Trivial solution of homogeneous linear equation is

(1,0,0,)

(0,0,0)

(0,0,1)

(0,1,0,0)

49. System of linear equations is inconsistent if:

System has one solution

None of these

System has no solution

System has two solutions

50.

Page 3 of 4

51.

±6

-6

52.

53.

54. We solve the system of non-homogeneous linear equations by:

a and b

c and a

a, b and c

b and c

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

2 x 5

2 x 3

3 x 2

5 x 2

56. If AB = BA = I and AC = CA = I then what about B and C.

Each is equal to A

None of these

They are not equal

They are equal

57. If the order of matrix A is m x p. And the order of B is p x n. Then the order of AB is?

m x n

n x p

n x m

m x p

58. The matrix A is Hermitian when (Ā)ᵗ =

Aᵗ

-A

59. In matrix multiplication for A and B, (AB)ᵗ is

A/B

BᵗAᵗ

1/AB

AᵗBᵗ

60.

61. If a system of equation has a unique solution or infinitely many solution then it is known as

Inconsistent

Nonlinear

None of these

Consistent

62.

None of these

a₁₁, a₂₁

a₁₁, a₁₂, a₁₃

a₂₁, a₂₂, a₂₃

63.

64. For non-trival solution |A| is:

A = 0

Aᵗ = 0

|A| = 0

Ā = 0

65. The square matrix A is skew-symmetric when Aᵗ = 0

-A

-B

-D

-C

66. The transpose of a square matrix is a

Scalar matrix

Square matrix

Diagonal matrix

Rectangular matrix

67. If B is additive inverse of A then

A + B = 0

A + B = A

A + B = B

B + A = I

68. (CD)ᵗ = ?

CᵗDᵗ

DᵗCᵗ

(DC)ᵗ

None

69. Two matrix A and B can be added if

Both have same order

Number of columns of A is equal to number of rows of B

Number of rows of A is equal to number of columns of B

Both are rectangular

70. The number of non-zero rows in an echlon form is called

Conjugate of the matrix

Cofactor of the matrix

Rank of a matrix

Reduced echlon form

71.

72. If A and B are two matrices such that AB = B and BA = A, then A² + B² =

A + B

2 BA

2 AB

73.

74. If a matrix has m rows and n columns then is order is

m x m

n x n

m x n

m + n

75. A square matrix A = [aij] is supper triangular when

aij = 0 for all i > j

dij = 0

cij = 0

bij = 0

Page 4 of 4

76.

Symmetric

Hermitian

Skew – symmetric

Skew-hermitian

77. Let A is a 3 x 3 matrix and B is its adjoint matrix. If |B| = 64, then |A| =

± 4

± 12

± 8

± 2

78. For a square matrix A if A² = A then A is called

Nilpotent matrix

Idempotent matrix

Periodic matrix

Symmetric matrix

79.

All

III only

II only

II & III only

80. An elementary row operation on a matrix A is

Multiplication of a column of a by any nonzero scalar

Interchange of any two rows of A

Interchange of any two columns of A

Addition of any multiple of one column to another column of A

81. For any non-Singular r matrix A, A¯¹ =

None of these

|A| adj A

1/|A|adj A

Adj A/|A|

82.

Then order of matrix A = ?

2 x 3

3 x 2

2 x 2

3 x 3

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Mustansar KhanLast Updated: October 15, 2025

Mathematics Matrices and Determinants Online Test

Important Math Matrices and Determinants Question and Answer

Math Matrices and Determinants Practice Test Online With Explanation

Math

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