Matrices Practice Questions - DPP for JEE

 Page 1


PART-I (Single Correct MCQs)
1. If A =  then A
100
 :
(a) 2
100
A
(b) 2
99
A
(c) 2
101
A
(d) None of these
2. If , then A
T
 + A = I
2
, if
(a)
(b)
(c)
(d) None of these
Page 2


PART-I (Single Correct MCQs)
1. If A =  then A
100
 :
(a) 2
100
A
(b) 2
99
A
(c) 2
101
A
(d) None of these
2. If , then A
T
 + A = I
2
, if
(a)
(b)
(c)
(d) None of these
3. If , I is the unit matrix of order 2 and a, b are arbitrary
constants, then (aI + bA)
2
 is equal to
(a) a
2
I + abA
(b) a
2
I + 2abA
(c) a
2
I + b
2
 A
(d) None of these
4. If f (a) =  and if a, ß, ?, are angle of a triangle, then f
(a). f (ß). f(?) equals
(a) I
2
(b) –I
2
(c) 0
(d) None of these
5. If A
a
 = , then
(a) A
a
 . A
(–a)
 = I
(b) A
a
 . A
(–a)
 = O
(c) A
a
 . A
ß 
= A
aß
(d) A
a
 . A
ß 
= A
a
 
–
 
ß
6. If A is a square matrix  such that (A – 2I) (A + I) = O, then A
–1
 =
(a)
(b)
(c) 2 (A – I)
(d) 2A + I
Page 3


PART-I (Single Correct MCQs)
1. If A =  then A
100
 :
(a) 2
100
A
(b) 2
99
A
(c) 2
101
A
(d) None of these
2. If , then A
T
 + A = I
2
, if
(a)
(b)
(c)
(d) None of these
3. If , I is the unit matrix of order 2 and a, b are arbitrary
constants, then (aI + bA)
2
 is equal to
(a) a
2
I + abA
(b) a
2
I + 2abA
(c) a
2
I + b
2
 A
(d) None of these
4. If f (a) =  and if a, ß, ?, are angle of a triangle, then f
(a). f (ß). f(?) equals
(a) I
2
(b) –I
2
(c) 0
(d) None of these
5. If A
a
 = , then
(a) A
a
 . A
(–a)
 = I
(b) A
a
 . A
(–a)
 = O
(c) A
a
 . A
ß 
= A
aß
(d) A
a
 . A
ß 
= A
a
 
–
 
ß
6. If A is a square matrix  such that (A – 2I) (A + I) = O, then A
–1
 =
(a)
(b)
(c) 2 (A – I)
(d) 2A + I
7. If  and Q = PAP
T
, then P (Q
2005
)P
T
 equal to
(a)
(b)
(c)
(d)
8. Let  and , . Then
(a) there cannot exist any B such that AB = BA
(b) there exist more than one but finite number of B's such that AB = BA
(c) there exists exactly one B such that AB = BA
(d) there exist infinitely many B's such that AB = BA
9. If A =  and I is the identity matrix of order 2, then (I
– A)  is equal to
(a) I + A
(b) I – A
(c) A – I
(d) A
10. If A is a square matrix such that A
2 
= I, then
Page 4


PART-I (Single Correct MCQs)
1. If A =  then A
100
 :
(a) 2
100
A
(b) 2
99
A
(c) 2
101
A
(d) None of these
2. If , then A
T
 + A = I
2
, if
(a)
(b)
(c)
(d) None of these
3. If , I is the unit matrix of order 2 and a, b are arbitrary
constants, then (aI + bA)
2
 is equal to
(a) a
2
I + abA
(b) a
2
I + 2abA
(c) a
2
I + b
2
 A
(d) None of these
4. If f (a) =  and if a, ß, ?, are angle of a triangle, then f
(a). f (ß). f(?) equals
(a) I
2
(b) –I
2
(c) 0
(d) None of these
5. If A
a
 = , then
(a) A
a
 . A
(–a)
 = I
(b) A
a
 . A
(–a)
 = O
(c) A
a
 . A
ß 
= A
aß
(d) A
a
 . A
ß 
= A
a
 
–
 
ß
6. If A is a square matrix  such that (A – 2I) (A + I) = O, then A
–1
 =
(a)
(b)
(c) 2 (A – I)
(d) 2A + I
7. If  and Q = PAP
T
, then P (Q
2005
)P
T
 equal to
(a)
(b)
(c)
(d)
8. Let  and , . Then
(a) there cannot exist any B such that AB = BA
(b) there exist more than one but finite number of B's such that AB = BA
(c) there exists exactly one B such that AB = BA
(d) there exist infinitely many B's such that AB = BA
9. If A =  and I is the identity matrix of order 2, then (I
– A)  is equal to
(a) I + A
(b) I – A
(c) A – I
(d) A
10. If A is a square matrix such that A
2 
= I, then
(A – I)
3
 + (A + I)
3
 – 7A is equal to
(a) A
(b) I – A
(c) I + A
(d) 3A
11. If B is an idempotent matrix, and A = I – B, then
(a) A
2
 = A
(b) A
2
 = I
(c) AB = I
(d) BA = I
12. Let  then  is equal to
(a)
(b)
(c)
(d)
13. For each real number x such that – 1 < x < 1, let A (x) be the matrix 
(a) A(z) = A(x) + A(y)
(b) A(z) = A(x)[A(y)]
–1
(c) A(z) = A(x) A(y)
(d) A(z) = A(x) – A(y)
14. If , then A
16
 is equal to :
Page 5


PART-I (Single Correct MCQs)
1. If A =  then A
100
 :
(a) 2
100
A
(b) 2
99
A
(c) 2
101
A
(d) None of these
2. If , then A
T
 + A = I
2
, if
(a)
(b)
(c)
(d) None of these
3. If , I is the unit matrix of order 2 and a, b are arbitrary
constants, then (aI + bA)
2
 is equal to
(a) a
2
I + abA
(b) a
2
I + 2abA
(c) a
2
I + b
2
 A
(d) None of these
4. If f (a) =  and if a, ß, ?, are angle of a triangle, then f
(a). f (ß). f(?) equals
(a) I
2
(b) –I
2
(c) 0
(d) None of these
5. If A
a
 = , then
(a) A
a
 . A
(–a)
 = I
(b) A
a
 . A
(–a)
 = O
(c) A
a
 . A
ß 
= A
aß
(d) A
a
 . A
ß 
= A
a
 
–
 
ß
6. If A is a square matrix  such that (A – 2I) (A + I) = O, then A
–1
 =
(a)
(b)
(c) 2 (A – I)
(d) 2A + I
7. If  and Q = PAP
T
, then P (Q
2005
)P
T
 equal to
(a)
(b)
(c)
(d)
8. Let  and , . Then
(a) there cannot exist any B such that AB = BA
(b) there exist more than one but finite number of B's such that AB = BA
(c) there exists exactly one B such that AB = BA
(d) there exist infinitely many B's such that AB = BA
9. If A =  and I is the identity matrix of order 2, then (I
– A)  is equal to
(a) I + A
(b) I – A
(c) A – I
(d) A
10. If A is a square matrix such that A
2 
= I, then
(A – I)
3
 + (A + I)
3
 – 7A is equal to
(a) A
(b) I – A
(c) I + A
(d) 3A
11. If B is an idempotent matrix, and A = I – B, then
(a) A
2
 = A
(b) A
2
 = I
(c) AB = I
(d) BA = I
12. Let  then  is equal to
(a)
(b)
(c)
(d)
13. For each real number x such that – 1 < x < 1, let A (x) be the matrix 
(a) A(z) = A(x) + A(y)
(b) A(z) = A(x)[A(y)]
–1
(c) A(z) = A(x) A(y)
(d) A(z) = A(x) – A(y)
14. If , then A
16
 is equal to :
(a)
(b)
(c)
(d)
15. If  is square root of identity matrix of order 2 then –
(a) 1 + a
2
 + ß? = 0
(b) 1 + a
2
 – ß? = 0
(c) 1 – a
2
 + ß? = 0
(d) a
2
 + ß? = 1
16. If A and B are matrices of same order, then  is a
(a) skew symmetric matrix
(b) null matrix
(c) symmetric matrix
(d) unit matrix
17. If A is symmetric as well as skew-symmetric matrix, then A is
(a) Diagonal
(b) Null
(c) Triangular
(d) None of these
18. If A and B are two square matrices such that
B = – A
–1
 BA, then  (A + B)
2
 =
(a) O
(b)
(c) + 2 AB +