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JEE Main Math Class 12 Matrices Part 1 Questions
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© examsnet.com
Question : 9
Total: 100
If
P
is a
3
×
3
real matrix such that
P
T
=
aP
+
(
a
−
1
)
I
, where
a
>
1
, then
[30-Jan-2023 Shift 2]
P
is a singular matrix
|
Adj
P
|
>
1
|
Adj
P
|
=
1
2
|
Adj
P
|
=
1
Validate
Solution:
P
T
=
aP
+
(
a
−
1
)
I
⇒
P
=
aP
T
+
(
a
−
1
)
I
⇒
P
T
−
P
=
a
(
P
−
P
T
)
⇒
P
=
P
T
,
as
a
≠
−
1
Now,
P
=
aP
+
(
a
−
1
)
I
⇒
P
=
−
I
⇒
|
P
|
=
1
⇒
|
Adj
P
|
=
1
© examsnet.com
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