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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

Page 1 of 4

Math

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

1 x 3

3 x 1

3 x 3

1 x 1

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

The principal diagonal

None of these

The secondary diagonal

Both a and b

4. Minimum number of equation for any system of equations

|A| ≠ 0

|A| = ∞

None of these

|A|= 0

Column matrix

Scalar matrix

Zero matrix

Diagonal matrix

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

∞

7. Trivial solution of homogeneous linear equation is

(0,0,1)

(0,0,0)

(0,1,0,0)

(1,0,0,)

8. The additive inverse of a matrix A is

-A

Adj A/|A|

A²

9. [-1, 4 7 2] is a

Scalar matrix

Column matrix

Diagonal matrix

Row matrix

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

2 AB

A + B

2 BA

11.

a = 2, b = 3

a = 3, b = 3

a = 3, b = 2

a = 2, b = 2

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

A/B

1/AB

AᵗBᵗ

BᵗAᵗ

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

b = 0, a = 0

a ≠ 0, b ≠ 0, k = 0

a = 0, b ≠ 0

a = -0, a ≠ 0

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

A = 0

|A| = 0

Aᵗ = 0

Ā = 0

15.

Identity matrix

Odd matrix

Even matrix

Scairar matrix

16. (AB)t = ?

AᵗBᵗ

BᵗAᵗ

17.

Skew-hermitian

Symmetric

Skew – symmetric

Hermitian

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

1/|A|adj A

None of these

|A| adj A

Adj A/|A|

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

bij = 0

cij = 0

dij = 0

aij = 0 for all i > j

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

Transpose

Non-symmetric

Matrix

Symmetric

21. 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

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

Inconsistent

Consistent

Nonlinear

None of these

23.

-1

24.

Zero matrix

Non – diagonal matrix

Identity matrix

Row matrix

25.

a₂₁, a₂₂, a₂₃

a₁₁, a₁₂, a₁₃

None of these

a₁₁, a₂₁

Page 2 of 4

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

A + B ≠ B + A

(A¹) ≠ A

AB ≠ BA

All are true

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

None of these

They are not equal

Each is equal to A

They are equal

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

a, b and c

c and a

a and b

b and c

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

None of these

Symmetric

Transpose

Inverse

30.

b²

b³

31.

±6

-6

32. If B is additive inverse of A then

A + B = B

A + B = A

B + A = I

A + B = 0

33.

Then order of matrix A = ?

2 x 3

3 x 3

3 x 2

2 x 2

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

B²

A²

35. 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

36.

37. Trival solution of homogeneous linear equation is:

(1, 3, 5)

a, b and c

(1, 1, 1)

(1, 2, 3)

38. [0 0 0] is

Identity matrix

Diagonal matrix

Null matrix

Scalar matrix

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

m x m

n x m

m x n

n x n

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

Diagonal matrix

-A

41. System of linear equations is inconsistent if:

None of these

System has two solutions

System has no solution

System has one solution

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

Idempotent matrix

Periodic matrix

Symmetric matrix

Nilpotent matrix

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

Non- singular matrix

Singular matrix

Zero matrix

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

-B

-A

-C

-D

45.

46. 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

47. For trival solution |A| is:

|A|≠ 0

A = 0

|A| = 0

48. The transpose of a square matrix is a

Scalar matrix

Square matrix

Diagonal matrix

Rectangular matrix

49. Equation having a common solution are called

Homogeneous equations

Linear equations

None of these

Simultaneous equation

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

2 x 3

2 x 5

5 x 2

3 x 2

Page 3 of 4

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

Scalar matrix

Identity matrix

Square matrix

Rectangular matrix

52. (CD)ᵗ = ?

DᵗCᵗ

CᵗDᵗ

(DC)ᵗ

None

53. 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

54. The transpose of a row matrix is a

Zero matrix

Column matrix

Scalar matrix

Diagonal matrix

55.

2 x 3

3 x 1

2 x 2

3 x 2

56.

3 x 2

3 x 3

2 x 3

2 x 2

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

m + n

m x m

n x n

m x n

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

Diagonal

Skew-symmetric

Symmetric

Null

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

Hermitian matrix

Identity

Symmetric

Scalar matrix

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

Aᵗ

-A

61.

62. (ABC)’ =

CBA

C’B’A

CBA’

C’B’A’

63. Two matrices A and B are equal if

Both have same order and equal corresponding elements

Both have same order

Both are rectangular

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

64.

Identity matrix

None of these

Diagonal matrix

Scalar matrix

65.

66.

III only

II & III only

II only

All

67.

68.

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

± 2

± 8

± 4

± 12

70. An elementary row operation on a matrix A is

Interchange of any two rows of A

Interchange of any two columns of A

Multiplication of a column of a by any nonzero scalar

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

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

-A

Aᵗ

72. 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

m x p

p x n

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

-A

Aᵗ

74.

-4

-6

None of these

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

Aij = 0 for all i < j

Bij = 0

Cij = 0

Dij = 0

Page 4 of 4

76.

77. Two matrix A and B can be added if

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

Both have same order

Both are rectangular

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

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

3/5

5/3

79. 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

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

Skew-symmetric

Null

Symmetric

None of the above

81.

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

A²

A³

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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