Question # 1

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Singular

Non-singular

Adjoint

None of above

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At

-A

A

A-1

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A(α) - A(β)

A(α) + A(β)

A(α-β)

A(α+β)

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A^-

A^t

-A

A

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3 x 1

1 x 3

3 x 3

1 x 1

Matrix multiplication is

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Commutative

Not commutative

Not associative

Not distributive

For trival solution |A| is

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A

|A| = 0

A = 0

|A|≠ 0

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2s²

2s³

s³

3s³

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3K

K2

K3

K

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

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A2

A3

A

None of above

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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Square matrix

Row matrix

Symmetric matrix

Null matrix

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0

1

2

3

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

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-3

-7

1

0

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a = 4, b = 1

a = 1, b = -4

a = 0, b = 4

a = 2, b = 4

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

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A²

A³

A

None of above

Rank of matrix [1 3 5 0] is

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1

3

2

4

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all are correct

If A and B are skew-symmetric then (AB)t is

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At Bt

AB

-AB

BA

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I

|A|

|A| I

None of these

Trival solution of homogeneous linear equation is

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(0, 0, 0)

(1, 2, 3)

(1, 3, 5)

a, b and c

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1

-1

0

I

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(2x4)

(2x7)

(2x3)

(7x2)

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

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

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Skew-symmetric

Symmetric

Null

Diagonal

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I3

rI3

r

none

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all

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

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