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UPSC NDA 2 2016 Mathematics Solved Paper
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© examsnet.com
Question : 28
Total: 120
A
=
[
1
−
1
2
3
]
and
B
=
[
2
3
−
1
−
2
]
then which of the following is/are correct?
1.
A
B
(
A
−
1
B
−
1
)
is a unit matrix.
2.
(
A
B
)
−
1
=
A
−
1
B
−
1
Select the correct answer using the code given below:
[NDA II 2016]
1 only
Both 1 only 2
2 only
Neither 1 nor 2
Validate
Solution:
A
=
[
1
−
1
2
3
]
and
B
=
[
2
3
−
1
−
2
]
|
A
|
=
3
−
(
−
2
)
=
5
and
|
B
|
=
−
4
−
(
−
3
)
=
−
1
⇒
A
−
1
=
1
5
[
3
1
−
2
1
]
and
B
−
1
=
−
1
[
−
2
−
3
1
2
]
A
B
=
[
3
5
1
0
]
and
A
−
1
B
−
1
=
1
5
[
5
7
−
5
8
]
⇒
A
B
(
A
−
1
B
−
1
)
=
1
5
[
−
10
−
12
5
7
]
≠
1
|
A
B
|
=
0
−
5
=
−
5
∴
(
A
B
)
−
1
=
−
1
5
[
0
−
5
−
1
3
]
≠
A
−
1
B
−
1
© examsnet.com
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