Question # 1

(ABC)' =

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CBA'

CBA

C'B'A

C'B'A'

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The number of non zero rows in echelon form of a matrix is called

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Order of matrix

Rank of matrix

Row operation

None of these

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Zero matrix

Diagonal matrix

Column matrix

Scalar matrix

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Matrix multiplication is

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Commutative

Not commutative

Not associative

Not distributive

The square matrix A is skew-symmetric when At =

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-B

-C

-A

-D

(ABC)' =

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CBA'

CBA

C' B' A'

None of these

The matrix A is Hermitian when (A)' =

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A

-A

A

A'

If A = |aij| is (m x n) matrix then transpose of A is of the order

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m x m

m x n

n x n

n x m

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System of linear equations is inconsistent if

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System has no solution

System has one solution

System has two solution

None of above

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(2x4)

(2x7)

(2x3)

(7x2)

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Orthogonal

Involutary

Idempotent

Nilpotent

A square matrix A = [aij] is upper triangular when

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cij = 0

bij = 0

aij = 0 for all i > j

dij = 0

If for the matrix A, A⁵= I, then A^-1=

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A²

A³

A

None of above

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5

15

10

20

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

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aij = 0 for all i < j

bij = 0

cij = 0

dij =0

For trival solution |A| is

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A

|A| = 0

A = 0

|A|≠ 0

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Scalar matrix

Identity matrix

Null matrix

Symmetric matrix

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

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2 AB

2 BA

A + B

AB

Which of the following is an identity matrix?

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none of these

A matrix with a single row is called a

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Column matrix

Row matrix

Null matrix

Identity matrix

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

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2 x 3

3 x 2

2 x 5

5 x 2

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A²- 5A + 7I = 1

2A²- 3A + 7I = 0

A²- 5A + I = 0

A²- 5A + 7I = 0

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At

-A

A

A-1

The transport of a null matrix is

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Row matrix

Column matrix

Square matrix

Null matrix

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

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0

1

-2

10

A and B be two square matrices and if their inverse exist, the (AB)^-1=

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A^-1B^-1

AB^-1

A^-1B

B^-1A^-1

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