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Byju's Answer
Standard XII
Mathematics
Adjoint of a Matrix
If A=[ 2 5...
Question
If
A
=
⎡
⎢
⎣
2
52
152
4
106
358
6
162
620
⎤
⎥
⎦
, then the determinant of the matrix
a
d
j
(
2
A
)
is equal to:
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Solution
∣
A
∣
=
∣
∣ ∣
∣
2
52
152
4
106
358
6
162
620
∣
∣ ∣
∣
=
0
We know that,
∣
a
d
j
(
A
)
∣
=
(
∣
A
∣
)
n
−
1
and,
∣
2
A
∣
=
2
n
∣
A
∣
∴
∣
a
d
j
(
2
A
)
∣
=
(
2
)
3
(
∣
A
∣
)
2
=
0
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0
Similar questions
Q.
Let
A
=
{
a
i
j
}
be a
3
×
3
matrix, where
a
i
j
=
⎧
⎪
⎨
⎪
⎩
(
−
1
)
j
−
i
if
i
<
j
,
2
if
i
=
j
,
(
−
1
)
i
+
j
if
i
>
j
,
then
det
(
3
A
d
j
(
2
A
−
1
)
)
is equal to
Q.
If
A
is an invertible matrix of order
n
, then the determinant of
adj
A
is equal to:
Q.
If the matrix A is such that
⎡
⎢
⎣
2
−
4
7
⎤
⎥
⎦
[
1
9
5
]
then the determinant of A is equal to
Q.
If
I
is unit matrix of order
10
, then the determinant of
I
is equal to
Q.
Let A be an orthogonal non-singular matrix of order n, then the determinant of matrix
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n
ie,
|
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−
I
n
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is equal to
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