Question # 1

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2

4

6

8

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

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If there are m rows and n columns in a matrix then its order is

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m x n

m x m

n x n

n x m

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

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At Bt

AB

-AB

BA

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For trival solution |A| is

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A

|A| is non zero

A = 0

None of these

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

A square matrix A for which A^t= -A is called a

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Column matrix

Symmetric matrix

Skew-symmetric matrix

Row matrix

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0

1

2

4

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

For any positive integer n

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ABn = Bn A ⇔ AB = BA

ABn = Bn A⇔ A,B are square matrices and AB = BA

ABn = BnA⇔ A + B

ABn = BnA ⇔ A and B are square matries

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all

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a = -1/2, b = -1

a = 1, b = 2

a = 2, b = 3

None of above

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1

-1

0

I

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

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Orthogonal

Involutary

Idempotent

Nilpotent

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5

15

10

20

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16

None of these

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3K

K2

K3

K

Matrix multiplication is

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Commutative

Not commutative

Not associative

Not distributive

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