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Byju's Answer
Standard XII
Mathematics
Definition of a Determinant
If A=[aij] ...
Question
If
A
=
[
a
i
j
]
is scalar matrix of order
n
×
n
such that
a
i
j
=
k
for all
i
, then
|
A
|
equals
A
n
k
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B
n
+
k
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C
n
k
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D
k
n
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Solution
The correct option is
D
k
n
For scalar matrix
∣
∣ ∣ ∣ ∣ ∣ ∣ ∣
∣
⎡
⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢
⎣
K
0
0
0
−
0
0
K
0
0
−
0
0
0
K
−
−
0
−
−
−
K
−
0
−
−
−
−
K
0
0
0
0
0
0
K
⎤
⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥
⎦
n
×
n
∣
∣ ∣ ∣ ∣ ∣ ∣ ∣
∣
=
K
n
Ans: D
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Similar questions
Q.
If
A
=
[
a
i
j
]
is a scalar matrix of order
n
×
n
such that
a
i
j
=
k
for all then trace of
A
is equal to
Q.
lf
A
=
[
a
i
j
]
is a scalar matrix of order
n
×
n
such that
a
i
j
=
k
for all
i
=
j
, then trace of
A
=
Q.
If A = [a
ij
] is a scalar matrix of order n × n such that a
ii
= k, for all i, then trace of A is equal to
(a) nk
(b) n + k
(c)
n
k
(d) none of these
Q.
Let
A
=
[
a
i
j
]
m
×
n
be a matrix such that
a
i
j
=
1
for all
i,j.
Then,
Q.
A square matrix
A
=
[
a
i
j
]
n
×
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, if
a
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for
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>
j
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then that matrix is known as
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