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NDA Math Matrices
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© examsnet.com
Question : 15
Total: 69
Let
A
=
[
0
2
−
2
0
]
and
(
m
I
+
n
A
)
2
=
A
where
m
,
n
are positive real numbers and
I
is the identity matrix. What is
(
m
+
n
)
equal to?
[NDA-II 2021]
0
1
2
1
3
2
Validate
Solution:
👈: Video Solution
(d) Let
A
=
[
0
2
−
2
0
]
and
(
m
l
+
n
A
)
2
=
A
where, / is Identify matrix
∵
m
l
+
n
A
=
m
[
1
0
0
1
]
+
n
[
0
2
−
2
0
]
=
[
m
0
0
m
]
+
[
0
2
n
−
2
n
0
]
=
[
m
2
n
−
2
n
m
]
∴
(
m
l
+
n
A
)
2
=
A
[
m
2
n
−
2
n
m
]
[
m
2
n
−
2
n
m
]
=
[
0
2
−
2
0
]
[
m
2
−
4
n
2
4
m
n
−
4
m
n
m
2
−
4
n
2
]
=
[
0
2
−
2
0
]
⇒
4
m
n
=
2
and
m
2
−
4
n
2
=
0
m
n
=
1
2
and
m
=
±
2
n
When,
m
=
2
n
(
2
n
)
(
n
)
=
1
2
n
=
±
1
2
⇒
m
=
±
1
∴
m
+
n
=
1
+
1
2
=
3
2
Hence, option (d) is correct.
© examsnet.com
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