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

B²

A²

3. The transpose of a row matrix is a

Scalar matrix

Diagonal matrix

Column matrix

Zero matrix

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

dij = 0

bij = 0

cij = 0

aij = 0 for all i > j

5. (AB)t = ?

BᵗAᵗ

AᵗBᵗ

6. Equation having a common solution are called

None of these

Simultaneous equation

Linear equations

Homogeneous equations

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

A = 0

|A| = 0

Ā = 0

Aᵗ = 0

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

1/|A|adj A

|A| adj A

None of these

Adj A/|A|

9. 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

3 x 2

5 x 2

2 x 5

10.

11.

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

None of these

Both a and b

The secondary diagonal

The principal diagonal

13. An elementary row operation on a matrix A is

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

Interchange of any two rows of A

Multiplication of a column of a by any nonzero scalar

Interchange of any two columns of A

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

B¯¹A¯¹

AB¯¹

A¯¹B¯¹

A¯¹B

15. 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 are rectangular

Both have same order

16.

a₁₁, a₁₂, a₁₃

a₁₁, a₂₁

None of these

a₂₁, a₂₂, a₂₃

17.

b²

b³

18. [-1, 4 7 2] is a

Column matrix

Diagonal matrix

Row matrix

Scalar matrix

19. 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

Skew-symmetric

Symmetric

20.

21. For trival solution |A| is:

|A|≠ 0

|A| = 0

A = 0

22. The transpose of a square matrix is a

Scalar matrix

Rectangular matrix

Diagonal matrix

Square matrix

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

3/5

5/3

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

-B

-A

-C

-D

25.

Scairar matrix

Odd matrix

Identity matrix

Even matrix

Page 2 of 4

26.

Then order of matrix A = ?

3 x 3

3 x 2

2 x 3

2 x 2

27. Trival solution of homogeneous linear equation is:

(1, 2, 3)

(1, 3, 5)

(1, 1, 1)

a, b and c

28. 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

29. [0 0 0] is

Scalar matrix

Null matrix

Identity matrix

Diagonal matrix

30.

-1

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

Symmetric

None of the above

Skew-symmetric

Null

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

None of these

A³

A²

33.

Zero matrix

Diagonal matrix

Scalar matrix

Column matrix

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

A + B ≠ B + A

All are true

AB ≠ BA

(A¹) ≠ A

35.

±6

-6

36.

37.

a = 3, b = 2

a = 3, b = 3

a = 2, b = 2

a = 2, b = 3

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

Zero matrix

Non- singular matrix

Singular matrix

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

-A

Aᵗ

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

± 4

± 12

± 2

± 8

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

∞

42. (CD)ᵗ = ?

CᵗDᵗ

None

DᵗCᵗ

(DC)ᵗ

43. If B is additive inverse of A then

B + A = I

A + B = B

A + B = A

A + B = 0

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

Square matrix

Rectangular matrix

Identity matrix

Scalar matrix

45. 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

I only

II and III

I and III

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

Dij = 0

Bij = 0

Aij = 0 for all i < j

Cij = 0

47. Trivial solution of homogeneous linear equation is

(0,1,0,0)

(1,0,0,)

(0,0,1)

(0,0,0)

48.

All

III only

II & III only

II only

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

-A

Aᵗ

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

Transpose

Matrix

Symmetric

Non-symmetric

Page 3 of 4

51. (ABC)’ =

CBA

C’B’A

C’B’A’

CBA’

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

AᵗBᵗ

BᵗAᵗ

A/B

1/AB

53.

3 x 1

2 x 3

2 x 2

3 x 2

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

Aᵗ

-A

55.

56.

Hermitian

Skew – symmetric

Skew-hermitian

Symmetric

57.

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

-A

Diagonal matrix

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

Transpose

None of these

Symmetric

Inverse

60. 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

61.

Row matrix

Non – diagonal matrix

Zero matrix

Identity matrix

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

m x m

m + n

m x n

n x n

63. System of linear equations is inconsistent if:

System has no solution

None of these

System has two solutions

System has one solution

64.

65. The additive inverse of a matrix A is

-A

Adj A/|A|

A²

66.

-6

-4

None of these

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

Rank of a matrix

Reduced echlon form

Cofactor of the matrix

Conjugate of the matrix

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

a and b

b and c

a, b and c

c and a

69.

Identity matrix

None of these

Scalar matrix

Diagonal matrix

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

Inconsistent

None of these

Consistent

Nonlinear

71.

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

Idempotent matrix

Symmetric matrix

Periodic matrix

Nilpotent matrix

73. Minimum number of equation for any system of equations

|A| = ∞

None of these

|A|= 0

|A| ≠ 0

74.

2 x 2

3 x 2

2 x 3

3 x 3

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

Symmetric

Identity

Scalar matrix

Hermitian matrix

Page 4 of 4

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

a = 0, b ≠ 0

b = 0, a = 0

a ≠ 0, b ≠ 0, k = 0

a = -0, a ≠ 0

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

A + B

2 AB

2 BA

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

1 x 1

1 x 3

3 x 1

3 x 3

79. Two matrices A and B are equal if

Both have same order and equal corresponding elements

Both are rectangular

Both have same order

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

80. 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 p

p x n

n x p

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

n x m

m x n

m x m

n x n

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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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