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JEE Main Math Class 12 Matrices Part 1 Questions
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© examsnet.com
Question : 98
Total: 100
If
A
=
[
2
3
0
−
1
]
, then the value of
det
(
A
4
)
+
det
[
A
10
−
Adj
(
2
A
)
10
]
is equal to
.
.
.
.
.
[17 Mar 2021 Shift 1]
Your Answer:
Validate
Solution:
If
A
=
[
2
3
0
−
1
]
d
e
t
(
A
4
)
+
d
e
t
[
A
10
−
[
A
d
j
(
2
A
)
]
10
]
A
⋅
A
=
[
2
3
0
−
1
]
[
2
3
0
−
1
]
=
[
4
3
0
1
]
A
=
[
2
3
0
−
1
]
,
A
2
=
[
4
3
0
1
]
A
3
=
A
2
⋅
A
=
[
4
3
0
1
]
[
2
3
0
−
1
]
=
[
8
9
0
−
1
]
A
4
=
A
3
⋅
A
=
[
8
9
0
−
1
]
[
2
3
0
−
1
]
=
[
16
15
0
1
]
A
n
=
[
2
n
2
n
−
(
−
1
)
n
0
(
−
1
)
n
]
A
10
=
[
2
10
2
10
−
1
0
1
]
⇒
2
A
=
[
4
6
0
−
2
]
a
d
j
(
2
A
)
=
[
−
2
−
6
0
4
]
a
d
j
(
2
A
)
=
−
2
(
1
3
0
−
2
)
[
∵
x
=
(
a
b
c
d
)
a
d
j
(
x
)
=
(
d
−
b
−
c
a
)
]
[
a
d
j
(
2
A
)
]
2
=
4
(
1
3
0
−
2
)
(
1
3
0
−
2
)
=
4
(
1
−
3
0
4
)
[
a
d
j
(
2
A
)
]
3
=
4
(
1
−
3
0
4
)
×
(
−
2
)
(
1
3
0
−
2
)
=
−
8
(
1
9
0
−
8
)
[
a
d
j
(
2
A
)
]
3
=
4
(
1
−
3
0
4
)
×
(
−
2
)
(
1
3
0
−
2
)
=
−
8
(
1
9
0
−
8
)
[
a
d
j
(
2
A
)
]
n
=
(
−
2
)
n
[
1
(
−
1
)
n
[
2
n
−
(
−
1
)
n
]
0
(
−
1
)
n
2
n
]
[
a
d
j
(
2
A
)
]
10
=
2
10
(
1
−
(
2
10
−
1
)
0
2
10
)
Now,
A
10
−
[
a
d
j
(
2
A
)
]
10
=
[
2
10
2
10
−
1
0
1
]
−
[
2
10
−
(
2
20
−
2
10
)
0
2
20
]
=
[
0
2
⋅
2
10
−
2
20
−
1
0
1
−
2
20
]
d
e
t
|
A
10
−
a
d
j
(
2
A
)
10
|
=
0
∴
d
e
t
(
A
4
)
+
d
e
t
[
A
10
−
a
d
j
(
2
A
)
10
]
=
(
16
)
4
+
0
=
16
© examsnet.com
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