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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. Matrix obtained by interchanging its rows and columns is called

None of these

Transpose

Inverse

Symmetric

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

Symmetric matrix

Nilpotent matrix

Periodic matrix

Idempotent matrix

3. Trivial solution of homogeneous linear equation is

(1,0,0,)

(0,0,1)

(0,0,0)

(0,1,0,0)

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

± 4

± 2

± 8

± 12

5. [-1, 4 7 2] is a

Column matrix

Diagonal matrix

Row matrix

Scalar matrix

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

Aᵗ

-A

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

All are true

A + B ≠ B + A

AB ≠ BA

(A¹) ≠ A

Zero matrix

Non – diagonal matrix

Identity matrix

Row matrix

9. 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 and equal corresponding elements

Both have same order

Both are rectangular

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

A¯¹B¯¹

B¯¹A¯¹

A¯¹B

AB¯¹

11. 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

12.

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

m + n

m x m

m x n

n x n

14. The transpose of a square matrix is a

Diagonal matrix

Rectangular matrix

Square matrix

Scalar matrix

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

A/B

BᵗAᵗ

1/AB

AᵗBᵗ

16. [0 0 0] is

Null matrix

Scalar matrix

Diagonal matrix

Identity matrix

17.

a₁₁, a₁₂, a₁₃

a₁₁, a₂₁

a₂₁, a₂₂, a₂₃

None of these

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

B²

A²

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

-A

-C

-B

-D

20.

All

III only

II & III only

II only

21.

Symmetric

Skew-hermitian

Hermitian

Skew – symmetric

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

n x p

p x p

p x n

m x p

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

None of the above

Null

Skew-symmetric

Symmetric

24. An elementary row operation on a matrix A is

Interchange of any two columns of A

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

Multiplication of a column of a by any nonzero scalar

Interchange of any two rows of A

25.

Page 2 of 4

26. System of linear equations is inconsistent if:

System has two solutions

System has one solution

System has no solution

None of these

27.

Scairar matrix

Identity matrix

Even matrix

Odd matrix

28.

Zero matrix

Scalar matrix

Diagonal matrix

Column matrix

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

Diagonal matrix

-A

30.

2 x 2

3 x 2

3 x 3

2 x 3

31. (ABC)’ =

C’B’A’

CBA

CBA’

C’B’A

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

∞

33. (CD)ᵗ = ?

CᵗDᵗ

DᵗCᵗ

None

(DC)ᵗ

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

None of these

The principal diagonal

The secondary diagonal

Both a and b

35.

a = 2, b = 2

a = 3, b = 2

a = 3, b = 3

a = 2, b = 3

36.

Then order of matrix A = ?

2 x 3

2 x 2

3 x 2

3 x 3

37. If B is additive inverse of A then

A + B = 0

A + B = B

A + B = A

B + A = I

38.

3 x 1

3 x 2

2 x 2

2 x 3

39.

Diagonal matrix

Scalar matrix

Identity matrix

None of these

40. 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

n x m

m x n

m x p

41.

42.

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

Identity matrix

Scalar matrix

Square matrix

Rectangular matrix

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

1 x 1

3 x 1

3 x 3

1 x 3

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

Ā = 0

|A| = 0

Aᵗ = 0

A = 0

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

cij = 0

bij = 0

aij = 0 for all i > j

dij = 0

47. Two matrix A and B can be added if

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 have same order

Both are rectangular

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

Dij = 0

Aij = 0 for all i < j

Cij = 0

Bij = 0

49. The transpose of a row matrix is a

Diagonal matrix

Zero matrix

Column matrix

Scalar matrix

50. 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

Page 3 of 4

51.

None of these

-4

-6

52.

b³

b²

53. For trival solution |A| is:

|A| = 0

A = 0

|A|≠ 0

54. The additive inverse of a matrix A is

-A

Adj A/|A|

A²

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

Aᵗ

-A

56.

-6

±6

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

3/5

5/3

58.

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

m x m

n x n

m x n

n x m

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

2 AB

2 BA

A + B

61.

62. (AB)t = ?

AᵗBᵗ

BᵗAᵗ

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

1/|A|adj A

None of these

Adj A/|A|

|A| adj A

64.

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

Nonlinear

Consistent

Inconsistent

None of these

66. 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

II and III

I and III

III only

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

Reduced echlon form

Cofactor of the matrix

Conjugate of the matrix

Rank of a matrix

68.

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

Hermitian matrix

Scalar matrix

Identity

Symmetric

70.

-1

71.

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

a = 0, b ≠ 0

a = -0, a ≠ 0

b = 0, a = 0

a ≠ 0, b ≠ 0, k = 0

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

a, b and c

a and b

c and a

b and c

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

Zero matrix

Singular matrix

Non- singular matrix

75. Trival solution of homogeneous linear equation is:

a, b and c

(1, 3, 5)

(1, 1, 1)

(1, 2, 3)

Page 4 of 4

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

-A

Aᵗ

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

Transpose

Non-symmetric

Matrix

Symmetric

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

They are not equal

Each is equal to A

None of these

They are equal

79. Minimum number of equation for any system of equations

|A|= 0

|A| = ∞

None of these

|A| ≠ 0

80. Equation having a common solution are called

Linear equations

Homogeneous equations

None of these

Simultaneous equation

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

None of these

Symmetric matrix

Diagonal matrix

Hermition matrix

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

A³

A²

None of these

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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

Math

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Mathematics Matrices and Determinants MCQS Online Test

ECAT Math Matrices and Determinants Chapter Online Test

Math Matrices and Determinants Test Online

Math

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Mustansar Khan

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