Question # 1

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

For trival solution |A| is

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A

|A| = 0

A = 0

|A|≠ 0

A matrix with a single row is called a

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Column matrix

Row matrix

Null matrix

Identity matrix

Let A be a square matrix. Then, 1/2 (A-A') is

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Skew-symmetric

Symmetric

Null

None of the above

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x =0, y =4

x = -1, y = 2

x = 2, y = 3

x = 3, y = 4

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A matrix in which the number of rows is 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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Identity matrix

Diagonal matrix

Null matrix

Hermitian matrix

Rank of matrix [1 3 5 0] is

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1

3

2

4

For a square matrix A, if A = A^t, then A is called

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matrix

Transpose

Symmetric

Non-symmetric

A diagonal matrix is always

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Identity

Triangular

Scalar

Non-singular

If A is a non-singular matrix then adj A is

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Non-singular

Symmetric

Singular

Non defined

If A is a non singular matrix then A^-1= ______

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3K

K2

K3

K

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

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

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

Which of the following is an identity matrix?

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none of these

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I3

rI3

r

none

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2 x 2

2 x 3

3 x 2

3 x 3

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(2x4)

(2x7)

(2x3)

(7x2)

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A(α) - A(β)

A(α) + A(β)

A(α-β)

A(α+β)

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1

0

3

-1

Trival solution of homogeneous linear equation is

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(0, 0, 0)

(1, 2, 3)

(1, 3, 5)

a, b and c

System of linear equation 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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3 x 2

2 x 3

3 x 3

2 x 2

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A^-

A^t

-A

A

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5

15

10

20

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