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UPSC NDA Math Model Paper 9
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© examsnet.com
Question : 25
Total: 120
Let
A
be a non-singular matrix of the order
2
×
2
then
|
A
−
1
|
=
|
A
|
1
|
A
|
0
None of these
Validate
Solution:
Let A is the second-order matrix,
As we know,
A
A
−
1
=
I
Taking determinants both sides, we get
⇒
det
(
A
A
−
1
)
=
det
I
⇒
det
(
A
−
1
)
×
det
(
A
)
=
1
[
∵
det
(
A
B
)
=
det
A
×
det
B
]
∴
det
(
A
−
1
)
=
1
det
(
A
)
=
1
|
A
|
© examsnet.com
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