If  and , then

a)

b)

c)

d)

If  are cube roots of unity, then
 is equal to

a) 0

b) b

c) ω

d)

If  is a cube root of unity, then  equals

a) 0

b) 1

c) i

d) ω

If the system of linear equations
x + 2ay + az =0
x + 3by + bz = 0
x + 4cy + cz = 0
has a non-zero solution, then a, b, c

a) are in arithmetic progression

b) are in geometric progression

c) are in harmonic progression

d) satisfy a + 2b + 3c = 0

If  then  is

a) –2

b) –1

c) 2

d) 1

The value of  is

a) 1

b) –1

c) –xyz

d) 0

The matrix  is

a) Unitary

b) Orthogonal

c) Nil potent

d) Involuntary

Let  where 0 ≤ ≤ 2 then the range of |A| is

a) 0

b) (2, 4)

c) [2, 4]

d) None of these

The question contains two statements : Statement 1(assertion) and Statement 2(reason). The question has four alternative choices, only one of which is the correct alternative. You have to select one of the codes a, b, c, d given below.
Statement 1: If a, b, c are distinct and x, y, z are not all zero and ax + by + cz = 0, bx + cy + az = 0, cx + ay + bz = 0
then a + b + c = 0
Statement 2:  if a, b, c are distinct.

a) Statement 1 is false. Statement 2 is true.

b) Statement 1 is true. Statement 2 is true. Statement 2 is a correct explanation of Statement 1.

c) Statement 1 is true. Statement 2 is true. Statement 2 is not a correct explanation of Statement 1.

d) Statement 1 is true. Statement 2 is false.

If A is a skew symmetric matrix then the trace of A is

a) 1

b) –1

c) 0

d) None of these

The arbitrary constant on which the value of the determinant
does not depend is

a) α

b) p

c) d

d) a

If  and A. Adj A = λI,
then the value of λ is

a) 2

b) 1

c) 3

d) 0

The value of  if
 is

a) 0

b) 1

c) –1

d) None of these

If  is the square root of a two rowed unit matrix then α, β and γ should satisfy the relation

a)

b)

c)

d) None of these

If A is a symmetric matrix then the matrix M’AM is

a) Symmetric

b) Skew symmetric

c) Orthogonal

d) None of the above

If the system of equations
ax + y + z = 0

x + by + z = 0, and

x + y + cz = 0
where a, b, c ≠ 1 has a non-trivial solution, then the value of

 is

a) –1

b) 0

c) 1

d) None of these

If x + y + z = 6, x – y + z = 2, 2x + y – z = 1 then x, y, z are respectively

a) 3, 2, 1

b) 2, 1, 3

c) 1, 2, 3

d) None of these

If a, b, c are positive integers then the determinant
 is divisible by

a)

b)

c)

d)

For the matrix which of the following is correct

a)

b)

c)

d)

Matrices A and B are such that

3A – 2B =  and

− .

Find A and B.

a)

b)

c)

If A is a skew symmetric matrix of odd order then the determinant of A is

a) –1

b) 0

c) 1

d) a real number

If  show that , where I, O are unit matrix and null matrix of order 3 respectively. Using the result find .

Prove that the product of matrices
 and  
is zero when  differ by an odd multiple of .