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
How to Attempt Test:	Please choose the right Option in MCQ-type question.
Test Helpful For:	ECAT Entry Test Math Online Test Interview Questions about Math All Universities Entrance Test Recruitments Tests

Math Matrices and Determinants Practice Test Online With Explanation

Please wait...

Page 1 of 4

Math

1. $Math 3. 21$

±6

-6

2. $Math 3. 02$

3. Trival solution of homogeneous linear equation is:

a, b and c

(1, 1, 1)

(1, 3, 5)

(1, 2, 3)

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

∞

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

None of these

Symmetric

Inverse

Transpose

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

Null

Diagonal

Symmetric

Skew-symmetric

7. $Math 3. 13$

Diagonal matrix

Scalar matrix

Zero matrix

Column matrix

8. $Math 3. 06$

Even matrix

Identity matrix

Odd matrix

Scairar matrix

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

a and b

a, b and c

c and a

b and c

10. (CD)ᵗ = ?

(DC)ᵗ

None

CᵗDᵗ

DᵗCᵗ

11. $Math 3. 04$

Skew – symmetric

Hermitian

Symmetric

Skew-hermitian

12. $Math 3. 11$

All

II only

II & III only

III only

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

Identity

Scalar matrix

Hermitian matrix

Symmetric

14. 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

5 x 2

2 x 5

3 x 2

2 x 3

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

5/3

3/5

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

Symmetric

Skew-symmetric

Null

None of the above

17. System of linear equations is inconsistent if:

None of these

System has one solution

System has no solution

System has two solutions

18. $Math 3. 23$

a = 3, b = 2

a = 3, b = 3

a = 2, b = 3

a = 2, b = 2

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

|A| adj A

Adj A/|A|

None of these

1/|A|adj A

20. (AB)t = ?

AᵗBᵗ

BᵗAᵗ

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

A³

None of these

A²

22. $Math 3. 03$ Then order of matrix A = ?

2 x 2

3 x 2

3 x 3

2 x 3

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

± 8

± 12

± 4

± 2

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

Dij = 0

Cij = 0

Bij = 0

Aij = 0 for all i < j

25. $Math 3. 16$

Page 2 of 4

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

The principal diagonal

The secondary diagonal

None of these

Both a and b

27. Trivial solution of homogeneous linear equation is

(0,0,0)

(0,0,1)

(0,1,0,0)

(1,0,0,)

28. Equation having a common solution are called

None of these

Simultaneous equation

Linear equations

Homogeneous equations

29. $Math 3. 10$

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

n x n

m x m

m x n

n x m

31. The transpose of a square matrix is a

Scalar matrix

Square matrix

Rectangular matrix

Diagonal matrix

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

All are true

A + B ≠ B + A

AB ≠ BA

(A¹) ≠ A

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

2 BA

A + B

2 AB

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

They are not equal

They are equal

Each is equal to A

None of these

35. $Math 3. 14$

36. Two matrices A and B are equal if

Both have same order

Both have same order and equal corresponding elements

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

Both are rectangular

37. If B is additive inverse of A then

A + B = B

A + B = 0

B + A = I

A + B = A

38. $Math 3. 15$

Identity matrix

Non – diagonal matrix

Row matrix

Zero matrix

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

1 x 3

1 x 1

3 x 1

3 x 3

40. Two matrix A and B can be added if

Both are rectangular

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

Both have same order

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

41. An elementary row operation on a matrix A is

Multiplication of a column of a by any nonzero scalar

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

Interchange of any two columns of A

Interchange of any two rows of A

42. The transpose of a row matrix is a

Diagonal matrix

Zero matrix

Scalar matrix

Column matrix

43. $Math 3. 12$

Identity matrix

Diagonal matrix

Scalar matrix

None of these

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

-A

Aᵗ

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

-A

Aᵗ

46. Minimum number of equation for any system of equations

|A|= 0

None of these

|A| ≠ 0

|A| = ∞

47. $Math 3. 24$

-1

48. 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

I only

II and III

III only

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

Nilpotent matrix

Symmetric matrix

Idempotent matrix

Periodic matrix

50. $Math 3. 07$

2 x 2

3 x 2

2 x 3

3 x 1

Page 3 of 4

51. $Math 3. 08$

b³

b²

52. $Math 3. 22$

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

a = -0, a ≠ 0

a ≠ 0, b ≠ 0, k = 0

a = 0, b ≠ 0

b = 0, a = 0

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

n x n

m x m

m x n

m + n

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

bij = 0

cij = 0

aij = 0 for all i > j

dij = 0

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

1/AB

AᵗBᵗ

BᵗAᵗ

A/B

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

-A

-C

-D

-B

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

A = 0

Ā = 0

|A| = 0

Aᵗ = 0

59. (ABC)’ =

CBA’

C’B’A’

C’B’A

CBA

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

-A

Diagonal matrix

61. The additive inverse of a matrix A is

Adj A/|A|

A²

-A

62. $Math 3. 18$

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

m x p

p x n

p x p

n x p

64. $Math 3. 09$

2 x 2

3 x 2

3 x 3

2 x 3

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

A²

B²

66. 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?

n x m

m x p

n x p

m x n

67. For trival solution |A| is:

|A|≠ 0

|A| = 0

A = 0

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

Symmetric

Transpose

Non-symmetric

Matrix

69. $Math 3. 20$

-4

-6

None of these

70. $Math 3. 05$

71. $Math 3. 19$

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

Aᵗ

-A

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

Consistent

Inconsistent

None of these

Nonlinear

74. $Math 3. 17$

a₁₁, a₂₁

a₂₁, a₂₂, a₂₃

None of these

a₁₁, a₁₂, a₁₃

75. [-1, 4 7 2] is a

Diagonal matrix

Scalar matrix

Column matrix

Row matrix

Page 4 of 4

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

A¯¹B

B¯¹A¯¹

A¯¹B¯¹

AB¯¹

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

Conjugate of the matrix

Cofactor of the matrix

Reduced echlon form

Rank of a matrix

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

Rectangular matrix

Scalar matrix

Identity matrix

Square matrix

79. $Math 3. 01$

80. [0 0 0] is

Null matrix

Diagonal matrix

Scalar matrix

Identity matrix

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

Hermition matrix

Diagonal matrix

None of these

Symmetric matrix

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

Singular matrix

Non- singular matrix

Zero matrix

More Related Resources

GAT Test Syllabus Paper Pattern For... Punjab Mathematics Online Test 11th... Punjab Mathematics Online Test 11th... Punjab Mathematics Online Test 11th... Punjab Mathematics Online Test 11th... Punjab Mathematics Online Test 11th... Punjab Mathematics Online Test 11th... Punjab Mathematics Online Test 11th... Punjab Mathematics Online Test 11th... PPSC Syllabus for Mathematics Lectu...

Can't find what you're looking for? Search below:

Latest Updates

GAT Test Syllabus Paper Pattern For General and GAT Subject
Punjab Mathematics Online Test 11th Class Model Paper Chapter No ...
Punjab Mathematics Online Test 11th Class Model Paper Chapter No ...
Punjab Mathematics Online Test 11th Class Model Paper Chapter No ...
Punjab Mathematics Online Test 11th Class Model Paper Chapter No ...
Punjab Mathematics Online Test 11th Class Model Paper Chapter No ...

Mustansar KhanLast Updated: October 15, 2025

Important Math Matrices and Determinants Question and Answer

Math Matrices and Determinants Practice Test Online With Explanation

Math

More Related Resources

Latest Updates

Mustansar Khan

Leave a Reply Cancel reply