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ECAT Mathematics Matrices and Determinants Online Test

Mustansar KhanLast Updated: April 18, 2025

Mathematics Matrices and Determinants MCQS Online Test

ECAT Math Matrices and Determinants Chapter Online Test

Total Questions:	82
Time Allowed:	40 Minutes
Total Marks:	82
How to Attempt Test:	Please choose the right Option in MCQ-type question.
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Math Matrices and Determinants Test Online

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Page 1 of 4

Math

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

Conjugate of the matrix

Reduced echlon form

Rank of a matrix

Cofactor of the matrix

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

Aᵗ

-A

-1

4. Equation having a common solution are called

Homogeneous equations

None of these

Simultaneous equation

Linear equations

Then order of matrix A = ?

3 x 2

2 x 3

2 x 2

3 x 3

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

Matrix

Symmetric

Transpose

Non-symmetric

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

Null

Symmetric

Diagonal

Skew-symmetric

8. Trival solution of homogeneous linear equation is:

a, b and c

(1, 2, 3)

(1, 3, 5)

(1, 1, 1)

9. 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 only

I and III

II and III

III only

10.

11.

Odd matrix

Even matrix

Scairar matrix

Identity matrix

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

Square matrix

Scalar matrix

Rectangular matrix

Identity matrix

13. The transpose of a row matrix is a

Column matrix

Zero matrix

Scalar matrix

Diagonal matrix

14.

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

None of these

Consistent

Nonlinear

Inconsistent

16.

Column matrix

Scalar matrix

Diagonal matrix

Zero matrix

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

Ā = 0

A = 0

|A| = 0

Aᵗ = 0

18. 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

n x p

m x p

p x p

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

Singular matrix

Non- singular matrix

Zero matrix

20.

b²

b³

21.

22.

II only

All

III only

II & III only

23.

None of these

Identity matrix

Scalar matrix

Diagonal matrix

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

Symmetric

Inverse

Transpose

None of these

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

Column matrix

Scalar matrix

Diagonal matrix

Row matrix

Page 2 of 4

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

(A¹) ≠ A

All are true

AB ≠ BA

A + B ≠ B + A

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

a = -0, a ≠ 0

b = 0, a = 0

a = 0, b ≠ 0

a ≠ 0, b ≠ 0, k = 0

28.

-4

None of these

-6

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

dij = 0

aij = 0 for all i > j

cij = 0

bij = 0

30. 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 p

m x p

n x m

m x n

31. [0 0 0] is

Null matrix

Scalar matrix

Diagonal matrix

Identity matrix

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

Symmetric matrix

Idempotent matrix

Periodic matrix

Nilpotent matrix

33.

3 x 1

3 x 2

2 x 3

2 x 2

34.

2 x 3

3 x 2

3 x 3

2 x 2

35.

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

A³

A²

None of these

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

B²

A²

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

Aᵗ

-A

39.

40. An elementary row operation on a matrix A is

Interchange of any two rows of A

Multiplication of a column of a by any nonzero scalar

Interchange of any two columns of A

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

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

Hermition matrix

Symmetric matrix

None of these

Diagonal matrix

42. (CD)ᵗ = ?

None

(DC)ᵗ

DᵗCᵗ

CᵗDᵗ

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

n x m

n x n

m x n

m x m

44.

45.

46. The transpose of a square matrix is a

Scalar matrix

Diagonal matrix

Square matrix

Rectangular matrix

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

2 AB

A + B

2 BA

48.

Skew – symmetric

Hermitian

Symmetric

Skew-hermitian

49. Trivial solution of homogeneous linear equation is

(0,0,0)

(0,1,0,0)

(1,0,0,)

(0,0,1)

50. The additive inverse of a matrix A is

A²

Adj A/|A|

-A

Page 3 of 4

51. 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

52.

53. 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

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

Symmetric

Hermitian matrix

Identity

Scalar matrix

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

± 4

± 2

± 8

± 12

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

∞

57. For trival solution |A| is:

A = 0

|A|≠ 0

|A| = 0

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

A/B

BᵗAᵗ

AᵗBᵗ

1/AB

59. Two matrix A and B can be added if

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

Both are rectangular

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

Both have same order

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

1 x 1

1 x 3

3 x 3

3 x 1

61.

62. System of linear equations is inconsistent if:

System has one solution

None of these

System has two solutions

System has no solution

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

|A| adj A

None of these

1/|A|adj A

Adj A/|A|

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

The secondary diagonal

None of these

Both a and b

The principal diagonal

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

c and a

b and c

a and b

a, b and c

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

-A

Aᵗ

67. Minimum number of equation for any system of equations

None of these

|A| ≠ 0

|A| = ∞

|A|= 0

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

5/3

3/5

69. Two matrices A and B are equal if

Both have same order and equal corresponding elements

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

Both are rectangular

Both have same order

70.

a = 2, b = 2

a = 2, b = 3

a = 3, b = 3

a = 3, b = 2

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

A¯¹B¯¹

AB¯¹

A¯¹B

B¯¹A¯¹

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

Null

None of the above

Symmetric

Skew-symmetric

73. (ABC)’ =

C’B’A

CBA

CBA’

C’B’A’

74.

Zero matrix

Non – diagonal matrix

Identity matrix

Row matrix

75. If B is additive inverse of A then

B + A = I

A + B = 0

A + B = B

A + B = A

Page 4 of 4

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

m x n

m x m

m + n

n x n

77.

a₁₁, a₂₁

None of these

a₂₁, a₂₂, a₂₃

a₁₁, a₁₂, a₁₃

78. (AB)t = ?

BᵗAᵗ

AᵗBᵗ

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

Diagonal matrix

-A

80.

±6

-6

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

Bij = 0

Aij = 0 for all i < j

Cij = 0

Dij = 0

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

-C

-D

-B

-A

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Mustansar KhanLast Updated: April 18, 2025

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ECAT Mathematics Matrices and Determinants Online Test

Mathematics Matrices and Determinants MCQS Online Test

ECAT Math Matrices and Determinants Chapter Online Test

Math Matrices and Determinants Test Online

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