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Question
Mathematics
Let A=[1 2 3 4] and B=[a 0 0 b] a, b ∈ N. Then,
Q. Let
A
=
[
1
3
2
4
]
and
B
=
[
a
0
0
b
]
a
,
b
∈
N
. Then,
768
162
Matrices
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A
there exists more than one but finite number of
B
′
s such that
A
B
=
B
A
B
there exists exactly one
B
such that
A
B
=
B
A
C
there exists infinitely many
B
′
s such that
A
B
=
B
A
D
there cannot exist any
B
such that
A
B
=
B
A
Solution:
Given that,
A
=
[
1
3
2
4
]
and
BB
=
[
a
0
0
b
]
Now,
A
B
=
[
1
3
2
4
]
[
a
0
0
b
]
=
[
a
3
a
2
b
4
b
]
and
B
A
=
[
a
0
0
b
]
[
1
3
2
4
]
=
[
a
3
b
2
a
4
b
]
If
A
B
=
B
A
, then
a
=
b
Hence,
A
B
=
B
A
is possible for infinitely many values of
B
.