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

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(2x4)

(2x7)

(2x3)

(7x2)

We solve 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

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 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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5

-5

none

The matrix A = [aij]mxn with m ≠n is always

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Symmetric

Hermition

Skew-symmetric

None

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

The transport of a rectangular matrix is a

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Square matrix

Rectangular matrix

Row matrix

Column matrix

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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

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

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The transpose of a column matrix is a ______

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Zero matrix

Diagonal matrix

Column matrix

Row matrix

The transport of a square matrix is a

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Row matrix

Column matrix

Square matrix

Null 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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3 x 2

2 x 3

3 x 3

2 x 2

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A(α) - A(β)

A(α) + A(β)

A(α-β)

A(α+β)

The transpose of a row matrix is a ______

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Zero matrix

Diagonal matrix

Column matrix

Row matrix

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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K/6

2K

3K

6K

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6, -12, -18

-6, 4, 9

-6, -4, -9

-6, 12, 18

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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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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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For a square matrix A, if A = At, then A is called

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Matrix

Transpose

Symmetric

Non-symmetric

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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Orthogonal

Involutary

Idempotent

Nilpotent

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4A - 3I

3A - 4I

A - I

None of these

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