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AIEEE 2006 Solved Paper
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© examsnet.com
Question : 133
Total: 143
Let
A
=
(
1
2
3
4
)
and
B
=
(
a
0
0
b
)
,
a
,
b
∈
N
. Then
there cannot exist any
B
such that
A
B
=
B
A
there exist more then one but finite number of
B
′
s such that
A
B
=
B
A
there exists exactly one
B
such that
A
B
=
B
A
there exist infinitely many
B
′
s such that
A
B
=
B
A
Validate
Solution:
A
=
[
1
2
3
4
]
B
=
[
a
0
0
b
]
A
B
=
[
a
2
b
3
a
4
b
]
B
A
=
[
a
0
0
b
]
[
1
2
3
4
]
=
[
a
2
a
3
b
4
b
]
Hence,
A
B
=
B
A
only when
a
=
b
∴
There can be infinitely many
B
′
s
for which
A
B
=
B
A
© examsnet.com
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