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

Square matrix

Rectangular matrix

Scalar matrix

Identity matrix

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

± 12

± 4

± 2

± 8

4. 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

5. (ABC)’ =

C’B’A’

CBA

CBA’

C’B’A

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

A³

None of these

A²

7. Equation having a common solution are called

Homogeneous equations

None of these

Simultaneous equation

Linear equations

8. The additive inverse of a matrix A is

A²

Adj A/|A|

-A

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

A¯¹B

AB¯¹

B¯¹A¯¹

A¯¹B¯¹

10.

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

a, b and c

a and b

b and c

c and a

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

B²

A²

13.

14.

-6

±6

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

2 AB

2 BA

A + B

16.

Identity matrix

None of these

Diagonal matrix

Scalar matrix

17.

a₁₁, a₁₂, a₁₃

a₂₁, a₂₂, a₂₃

a₁₁, a₂₁

None of these

18. (AB)t = ?

AᵗBᵗ

BᵗAᵗ

19. Two matrices A and B are equal if

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

Both are rectangular

Both have same order

Both have same order and equal corresponding elements

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

Aij = 0 for all i < j

Cij = 0

Bij = 0

Dij = 0

21. Trivial solution of homogeneous linear equation is

(0,1,0,0)

(1,0,0,)

(0,0,1)

(0,0,0)

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

Singular matrix

Non- singular matrix

Zero matrix

23.

24. The transpose of a row matrix is a

Zero matrix

Scalar matrix

Column matrix

Diagonal matrix

25.

a = 2, b = 2

a = 3, b = 3

a = 2, b = 3

a = 3, b = 2

Page 2 of 4

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

Scalar matrix

Identity

Hermitian matrix

Symmetric

27. If B is additive inverse of A then

A + B = B

B + A = I

A + B = A

A + B = 0

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

None of these

Adj A/|A|

1/|A|adj A

|A| adj A

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

1 x 1

3 x 3

3 x 1

1 x 3

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

None of these

Inverse

Symmetric

Transpose

31. 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

m x p

p x p

n x p

32.

Diagonal matrix

Scalar matrix

Zero matrix

Column matrix

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

Consistent

Nonlinear

None of these

Inconsistent

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

Aᵗ

-A

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

The principal diagonal

The secondary diagonal

Both a and b

None of these

36.

-4

None of these

-6

37.

3 x 3

3 x 2

2 x 2

2 x 3

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

Aᵗ = 0

Ā = 0

A = 0

|A| = 0

39. System of linear equations is inconsistent if:

System has two solutions

None of these

System has one solution

System has no solution

40. (CD)ᵗ = ?

(DC)ᵗ

CᵗDᵗ

None

DᵗCᵗ

41. 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

3 x 2

5 x 2

2 x 3

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

Skew-symmetric

Symmetric

Null

None of the above

43.

Zero matrix

Row matrix

Non – diagonal matrix

Identity matrix

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

b = 0, a = 0

a = 0, b ≠ 0

a ≠ 0, b ≠ 0, k = 0

a = -0, a ≠ 0

45.

b³

b²

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

-A

Diagonal matrix

47.

-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

III only

II and III

49. 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 p

n x m

m x n

n x p

50.

Symmetric

Hermitian

Skew-hermitian

Skew – symmetric

Page 3 of 4

51. The transpose of a square matrix is a

Rectangular matrix

Diagonal matrix

Scalar matrix

Square matrix

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

Diagonal matrix

Hermition matrix

None of these

Symmetric matrix

53.

54.

II & III only

II only

III only

All

55.

56.

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

∞

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

3/5

5/3

59. [-1, 4 7 2] is a

Scalar matrix

Column matrix

Row matrix

Diagonal matrix

60. For trival solution |A| is:

|A|≠ 0

|A| = 0

A = 0

61. Two matrix A and B can be added if

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

Both have same order

Both are rectangular

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

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

Cofactor of the matrix

Reduced echlon form

Conjugate of the matrix

Rank of a matrix

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

Symmetric

Non-symmetric

Matrix

Transpose

64.

65. Trival solution of homogeneous linear equation is:

(1, 1, 1)

a, b and c

(1, 2, 3)

(1, 3, 5)

66. 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

67.

Then order of matrix A = ?

3 x 3

2 x 3

2 x 2

3 x 2

68.

3 x 2

2 x 2

3 x 1

2 x 3

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

Symmetric matrix

Idempotent matrix

Periodic matrix

Nilpotent matrix

70. [0 0 0] is

Identity matrix

Null matrix

Scalar matrix

Diagonal matrix

71. Minimum number of equation for any system of equations

None of these

|A| = ∞

|A| ≠ 0

|A|= 0

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

-A

Aᵗ

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

m x m

n x n

m + n

m x n

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

1/AB

A/B

AᵗBᵗ

BᵗAᵗ

75.

Even matrix

Scairar matrix

Identity matrix

Odd matrix

Page 4 of 4

76. 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

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

None of these

They are equal

Each is equal to A

They are not equal

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

aij = 0 for all i > j

dij = 0

cij = 0

bij = 0

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

-A

Aᵗ

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

-B

-A

-C

-D

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

All are true

(A¹) ≠ A

AB ≠ BA

A + B ≠ B + 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

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