Question # 1

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

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A-1 B-1

AB-1

A-1B

B-1A-1

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0

1

-A

-1

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9/4

4/9

1

None of these

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At

-A

A

A-1

Cofactor of an element a_ijis defined by

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(-1)^i+j|A|

(-1)^i+jM_ij

(-1)^i+jM^-1

None of these

We also the system of non-homogeneous linear equations by

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a and b

b and c

c and a

a, b and c

The transport of a null matrix is

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Row matrix

Column matrix

Square matrix

Null matrix

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

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A²

A³

A

None of above

The order of the matrix [1 2 3] is

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1 x 1

3 x 3

3 x 1

1 x 3

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A matrix with a single column is called

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Column matrix

Row matrix

Identity matrix

Null matrix

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Zero matrix

Diagonal matrix

Column matrix

Scalar matrix

If A = [a_ij] 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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I

14 I

0

None of these

A matrix in which the number of rows is not equal to the number of columns is called a

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Diagonal matrix

Rectangular matrix

Square matrix

Scalar matrix

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0

Independent of a

Independent of b

Independent of c

The transport of a square matrix is a

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Row matrix

Column matrix

Square matrix

Null matrix

If the matrices A and B have the order 1 x 10 and 10 x 1 then order of AB is

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1 x 1

1 x 10

10 x 10

10 x 1

The transpose of a row matrix is a ______

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Zero matrix

Diagonal matrix

Column matrix

Row matrix

A square matrix all of whose elements except the main diagonal are zeros is called a

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Null matrix

Singular matrix

Symmetric matrix

Diagonal matrix

A = [3] is a/an

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Square matrix

Scalar matrix

Diagonal matrix

Identity matrix

Which of the following is an identity matrix?

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none of these

Cofactor of an element aij denoted by Aij is

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(-2)i+j

Mij

(-1)i+j Mij

None of above

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

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BA

A2

AB

B2

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16

256

64

1024

A diagonal matrix in which the diagonal elements are equal is called a

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Null matrix

Identity matrix

Scalar matrix

Row matrix

A non-homogeneous linear system AX = B has no solution if

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|A| = 0

|A|≠ 0

Rank (a) = no of variables

Rank > no of variables

If the trace of matrix A is 5, then the trace of the matrix 3A is

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3/5

5/3

8

15

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0

1

2

3

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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