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JEE Main Math Class 12 Matrices Part 1 Questions
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© examsnet.com
Question : 35
Total: 100
Let
A
be a
3
×
3
invertible matrix. If
|
adj
(
24
A
)
|
=
|
adj
(
3
adj
(
2
A
)
)
|
, then
|
A
|
2
is equal to :
[26-Jun-2022-Shift-1]
6
6
2
12
2
6
1
Validate
Solution:
👈: Video Solution
We know,
|
adj
A
|
=
|
A
|
n
−
1
Now,
|
a
d
j
24
A
|
=
|
a
d
j
3
(
a
d
j
2
A
)
|
⇒
|
24
A
|
3
−
1
=
|
3
a
d
j
2
A
|
3
−
1
⇒
|
24
A
|
2
=
|
3
a
d
j
2
A
|
2
Also, we know,
|
K
A
|
=
K
n
|
A
|
⇒
(
(
24
)
2
)
2
|
A
|
2
=
(
(
3
)
3
)
2
|
a
d
j
2
A
|
2
⇒
(
24
)
6
|
A
|
2
=
3
6
⋅
(
|
2
A
|
3
−
1
)
2
⇒
(
24
)
6
|
A
|
2
=
3
6
⋅
|
2
A
|
4
⇒
(
24
)
6
|
A
|
2
=
3
6
⋅
(
2
3
)
4
⋅
|
A
|
4
⇒
3
6
⋅
8
6
⋅
|
A
|
2
=
3
6
⋅
8
4
⋅
|
A
|
4
⇒
8
2
=
|
A
|
2
⇒
|
A
|
2
=
64
=
2
6
© examsnet.com
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