Matrices & Determinants MCQs Part II

1) If the system of equations x + ay + az = 0, bx + y + bz = 0, cx + cy +
z = 0 Where a, b and c are non-zero and non-unity, has a non- trivial solution,
then the value of

a) zero
b) 1
c) -1
d)

2) If
then the value of is

a) 1
b) 2
c) 4
d) 3

3) If in
then
is

a) 0
b) -D
c) D
d)

4) Inverse of is
a)
b)
c)
d) none of these

5)
a) 1
b) 0
c) 3
d) a + b+ c

6) A and B are square matrices of order
is equal to

a)
b)
c)
d)

7) If
Then
is equal to

a) 0
b) 1
c) 100
d) -100

8) If ,
then

a) 5A
b) 10A
c) 16 A
d) 32 A

9) If
the value of x which satisfies the equation
is

a) x = a
b) x = b
c) x = c
d) x=0

10) If is
cube root of unity , then

a)
b)
c)
d)

11) If the system of equation x + 2 y – 3 z = 2, ( K+3) z = 3, (2K+1)y+z=2 is inconsistent , then K is
a) -2
b)
c) 1
d) 2

12) If the equations x- Ky – z = 0, Kx- y – z = 0, x+ y – z = 0 has a non zero solution, then the possible values of K are
a) -1, 2
b) 1, 2
c) 0, 1
d) -1, 1

13) The parameter on which the values of the determinantdoes not depend upon
a) a
b) p
c) d
d) x

14) If A, B, C are the angles of a triangle ABC, then the determinant
is equal to

a) 1
b) -1
c) sin A + sin B + sin C
d) none of these

15) If a, b, c are different, then the value of x satisfying
a) a
b) b
c) c
d) 0

16) The value of the determinant
a) k (a + b)(b + c) (c + a)
b)
c) k(a – b)(b – c)(c – a)
d) k(a + b – c)(b + c – a)(c + a – b)

17) If are
any four real numbers, then the determinant

a) 1
b) 0
c) 2
d) 3

18) If B is a non-singular matrix and A is a square matrix, then
is equal to

a) det (B)
b) det (A)
c)
d)

19) If
and nN,
then
is equal to

a)
b)
c) n A
d) none of these

20) If A =is
a scalar matrix of order n x n such that
= k for all I, then is
equal to

a) n k
b) n + k
c)
d)

21) If A is an orthogonal matrix, then is
equal to

a) A
b)
c)
d) None of these

22) If A is an orthogonal matrix, then
a)
b)
c)
d) none of these

23) If =then
t is equal to

a) 33
b) 21
c) 31
d) 23

24) If for AX = B, and
then
X is equal to

a)
b)
c)
d)

25)
a)
b)
c)
d) none of these

26) The value of determinant is
equal to

a)
b)
c)
d)

27) The value of determinant
is
equal to

a)
b)
c)
d)

28) ,
then is
equal to

a)
b)
c)
d) 9 tan x sec x

29) If,
then

a)
b)
c)
d)

30) If then is
equal to

a)
b)
c)
d)

31) The matrix A satisfying the equationA
=is

a)
b)
c)
d) None of these

32) If A is an orthogonal matrix, then equals
a) A
b)
c)
d) None of these

33)
a) D
b)
c)
d) None of these

34) If A and B are two invertible matrices, then the inverse of AB is equal to
a) AB
b) BA
c)
d)

35) If A,B,C are invertible matrices, then
is equal to

a)
b)
c)
d)

36) If
And then
n equals

a) 4
b) 6
c) 8
d) none of these

37) If A=diag (
a)
b)
c) A
d) None of these

38) If A = [aij]
is a skew-symmetric matrix of order n, then is

a) 0 for some i
b)
c) 1 for some i
d)

39) If A and B are matrices of the same order,then
is possible, if

a) AB=I
b) BA = I
c) AB=BA
d) None of these

40)
a) 17
b) 25
c) 3
d) 12

41) If A is a skew-symmetric matrix, then trace of A is
a) 1
b) -1
c) 0
d) None of these

42) If A,B are square matrices of the same order,then adj(AB) is equal to

43) If A is a square matrix of order and
k is a scalar, then adj(KA) is equal to

b)
c)
d)

44) If A is a square matrix or order then

a)
b)
c)
d)

45) and

a) sinx cosx
b) 1
c) 2
d) 3

46) If
a)
b)
c) n A
d) none of these

47)
a)
b)
c)
d)

48) If
then the value of k is

a) 3
b) 5
c) 7
d) -7

49) If A,B are two square matrics such that AB= A and BA= B, then
a) A,B are idempotent
b) Only A is idempotent
c) Only B is idempotent
d) None of these

50) The inverse of a symmetric matrix is
a) symmetric
b) skew-symmetric
c) diagonal matrix
d) none of these

51) If
is a scalar matrix of order such
that

a) nk
b) n+k
c)
d)

52) If
is a square matrix of order and
k is scalar, then

a)
b)
c)
d) none of these

53) Let F (a)
, Where
Then
equals

a)
b)
c)
d) none of these

54) If F(x)
then

a)
b)
c)
d)

55)
a) a=1, b=1
b)
c)
d) none of these

56) If matrix A is such that
then
is equal to

a)
b)
c)
d) none of these

57) A and B be
matrices. Then AB=0 implies

a) A=0 and B=0
b)
c)
d) A=0 or B=0

58) Which of the following is incorrect
a)
b)
c)
d)

59) If A is an invertible matrix, then which
of following is correct

a)
b)
c)
d)

60) If for a matrix
where I is the identity matrix, then A equals

a)
b)
c)
d)

61) Let A be a skew-symmetric matrix of odd order, then
a) 0
b) 1
c) -1
d) None of these

62) Let A be a non-singular square matrix. Then
a)
b)
c)
d) none of these

63) Let
be a square matrix,and let
be cofactor of

a)
b)
c)
d) none of these

64)
be a matrix such that

a) rank (A) >1
b) rank (A)=1
c) rank (A)=m
d) rank (A)=n

65) The rank of the matrix
a) 1
b) 2
c) 3
d) 4

66) If
is a matrix of rank r, then

a) r=min (m,n)
b) r < min (m,n)
c)
d) none of these

67) is
a matrix of rank r and B is a square submatrix of order r+1, then

a) B is invertible
b) B is not invertible
c) B may or may not be invertible
d) None of these

68) Let A be a skew-symmetric matrix of even order, then
a) is a square
b) is not a square
c) is always zero
d) none of these

69) If A is a non-singular square matrix of order n, then the
rank of A is

a) equal to n
b) less than n
c) greater than n
d) none of these

70) If A is a non-zero column matrix of order and
B is non-zero row matrix of order
then rank of AB equals

a) m
b) n
c) 1
d) none of these

71) If A and B are two matrices such that AB=B and BA=A, then

a) 2AB
b) 2BA
c) A+B
d) AB

72) If
a)
b)
c)
d)

73) If
a)
b)
c)
d) none of these

74) If
a) 3
b) 5
c) 2
d) 4

75) The system of linear equations x+y+z=2, 2x+y-z=3, 3x+2y+kz=4
has a unique solution if

a)
b) -1c) -2d) k=0

76) If A and B are square matrices of order 3 such that
a) -9
b) -81
c) -27
d) 81

77) If A is
and B=
then AB is said to be a square matrix of order

a)
b)
c)
d)

78) In an upper triangular matrix
the element
for

a)
b)
c)
d)

79) If A and B are arbitrary square matrices of same order, then
a)
b)
c)
d)

80) Let A be a square matrix. Then which of the following is not a symmetric
matric

a)
b)
c)
d)

81) If A is of order
and B is of order ,
then AB is of order

a)
b)
c)
d)

82) Let
Where
then
is equal to

a) i
b)
c)
d) -i

83) If
then

a)
b)
c)
d) none of these

84) If
then x equals

a) 1, 1, 0
b) 0, -1, 1
c) 1, -1, 3
d) 0, 0, 3

85) If ,
one value of x which satisfies the equation.

a) x = a
b) x = b
c) x = c
d) x = 0

86) Which one of the following determinant has its value as zero?
a)
b)
c)
d)

87) The value of
a) a + b + c – 3 abc
b) 3 (a +b) (b + c ) (c + a)
c) (a – b) (b – c) (c – a )
d) (a – b ) (b – c ) (c – a ) (a +b + c )

88) The value of satisfying

a)
b)
c)
d)

89) The repeated factor of the determinant
a) (x – y)
b) (y – z)
c) (z – x)
d) none of these

90) The value of
a)
b)
c)
d)

91) If p, q, r are negative distinct real numbers, then the determinant
a) < 0
b)
c) 0
d) > 0

92) The value of
a) 20
b) -2
c) 0
d) 5

93) One of the roots of
a) 6
b) 0
c) 3
d) -3

94) If
is an imaginary cube root of unity, then

a) 1
b) -1
c) 0
d) none of these

95) The value of det
a)
b) 0
c)
d) none of these

96) The value of the determinant
a) 2 (a+b+c)
b)
c) ab+bc+ca
d) 2 abc (ab+bc+ca)

97) If is
the transpose of a square matrix A, then

a)
b)
c)
d)

98) If a square matrix A has two identical rows or columns, then det A
is

a) 0
b) 1
c) -1
d) none of these

99) Let
a)
b)
c)
d) none of these

100) If A is square matrix such that
then det (A) equals

a) 0 or 1
b) -2 or 2
c) -3 or 3
d) none of these