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Question
Mathematics
Let A be a 3 × 3 matrix such that | operatornameadj( operatornameadj( operatornameadj A ))|=124 Then mid A -1 adj A mid is equal to
Q. Let
A
be a
3
×
3
matrix such that
∣
adj
(
adj
(
adj
A
))
∣
=
1
2
4
Then
∣
A
−
1
adj
A
∣
is equal to
269
152
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JEE Main 2023
Determinants
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A
1
0%
B
6
0%
C
12
14%
D
2
3
86%
Solution:
Given
∣
adj
(
adj
(
adj
.
A
))
∣
=
1
2
4
⇒
∣
A
∣
(
n
−
1
)
3
=
1
2
4
Given
n
=
3
⇒
∣
A
∣
8
=
1
2
4
⇒
∣
A
∣
2
=
12
∣
A
∣
=
2
3
We are asked
∣
∣
A
−
1
⋅
adj
A
∣
∣
=
∣
∣
A
−
1
∣
∣
⋅
∣
adj
A
∣
=
∣
A
∣
1
⋅
∣
A
∣
3
−
1
=
∣
A
∣
=
2
3