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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

2 x 2

2 x 3

3 x 2

3 x 1

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

Both a and b

The secondary diagonal

None of these

The principal diagonal

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

B¯¹A¯¹

A¯¹B¯¹

AB¯¹

A¯¹B

-1

b³

b²

6. 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 m

m x p

n x p

None of these

-4

-6

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

Square matrix

Scalar matrix

Identity matrix

Rectangular matrix

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

Scalar matrix

Identity

Symmetric

Hermitian matrix

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

A/B

BᵗAᵗ

AᵗBᵗ

1/AB

12.

a₁₁, a₂₁

None of these

a₂₁, a₂₂, a₂₃

a₁₁, a₁₂, a₁₃

13. [-1, 4 7 2] is a

Row matrix

Diagonal matrix

Column matrix

Scalar matrix

14. (AB)t = ?

BᵗAᵗ

AᵗBᵗ

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

AB ≠ BA

(A¹) ≠ A

All are true

A + B ≠ B + A

16.

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

3/5

5/3

18.

19. 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

20. 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

III only

II and III

I only

I and III

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

Singular matrix

Zero matrix

Non- singular matrix

22. 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 3

5 x 2

2 x 5

3 x 2

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

Aij = 0 for all i < j

Bij = 0

Dij = 0

Cij = 0

24.

Even matrix

Identity matrix

Odd matrix

Scairar matrix

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

b and c

c and a

a and b

a, b and c

Page 2 of 4

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

They are equal

Each is equal to A

None of these

They are not equal

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

A³

A²

None of these

28.

3 x 3

3 x 2

2 x 2

2 x 3

29.

Hermitian

Skew-hermitian

Skew – symmetric

Symmetric

30. Equation having a common solution are called

None of these

Simultaneous equation

Linear equations

Homogeneous equations

31. The transpose of a square matrix is a

Rectangular matrix

Scalar matrix

Square matrix

Diagonal matrix

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

m + n

m x n

n x n

m x m

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

∞

34. System of linear equations is inconsistent if:

System has one solution

System has no solution

System has two solutions

None of these

35. The transpose of a row matrix is a

Diagonal matrix

Zero matrix

Column matrix

Scalar matrix

36.

Then order of matrix A = ?

2 x 3

2 x 2

3 x 3

3 x 2

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

Skew-symmetric

Symmetric

None of the above

Null

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

Symmetric matrix

None of these

Diagonal matrix

Hermition matrix

39. (CD)ᵗ = ?

None

DᵗCᵗ

CᵗDᵗ

(DC)ᵗ

40. Two matrices A and B are equal if

Both have same order and equal corresponding elements

Both are rectangular

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

Both have same order

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

Inconsistent

None of these

Consistent

Nonlinear

42. [0 0 0] is

Identity matrix

Scalar matrix

Null matrix

Diagonal matrix

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

a ≠ 0, b ≠ 0, k = 0

a = 0, b ≠ 0

a = -0, a ≠ 0

b = 0, a = 0

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

-A

Aᵗ

45.

Zero matrix

Non – diagonal matrix

Identity matrix

Row matrix

46. Trivial solution of homogeneous linear equation is

(1,0,0,)

(0,1,0,0)

(0,0,0)

(0,0,1)

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

3 x 1

3 x 3

1 x 1

1 x 3

48. For trival solution |A| is:

|A|≠ 0

|A| = 0

A = 0

49.

Zero matrix

Scalar matrix

Diagonal matrix

Column matrix

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

None of these

Transpose

Inverse

Symmetric

Page 3 of 4

51.

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

Diagonal matrix

-A

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

Aᵗ

-A

54.

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

A²

B²

56.

a = 2, b = 3

a = 3, b = 2

a = 3, b = 3

a = 2, b = 2

57. Trival solution of homogeneous linear equation is:

a, b and c

(1, 2, 3)

(1, 1, 1)

(1, 3, 5)

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

|A| = 0

Ā = 0

Aᵗ = 0

A = 0

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

|A| adj A

None of these

Adj A/|A|

1/|A|adj A

60.

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

Nilpotent matrix

Periodic matrix

Symmetric matrix

Idempotent matrix

62.

±6

-6

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

Transpose

Symmetric

Matrix

Non-symmetric

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

bij = 0

aij = 0 for all i > j

dij = 0

cij = 0

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

Skew-symmetric

Symmetric

Diagonal

Null

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

-A

Aᵗ

67.

Identity matrix

Diagonal matrix

Scalar matrix

None of these

68. (ABC)’ =

CBA’

C’B’A

C’B’A’

CBA

69.

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

-B

-A

-C

-D

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

2 BA

A + B

2 AB

72.

73. Minimum number of equation for any system of equations

|A| ≠ 0

|A| = ∞

None of these

|A|= 0

74.

II only

All

III only

II & III only

75. If B is additive inverse of A then

A + B = 0

A + B = B

A + B = A

B + A = I

Page 4 of 4

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

± 4

± 2

± 8

± 12

77. The additive inverse of a matrix A is

Adj A/|A|

A²

-A

78. 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 p

p x n

m x p

n x p

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

m x n

n x n

m x m

n x m

80. 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

81. 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

82.

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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

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