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Byju's Answer
Standard XII
Mathematics
Scalar Matrix
Two n × n s...
Question
Two
n
×
n
square matrices
A
and
B
are said to be similar if there exists a non-singular matrix
P
such that
P
−
1
A
P
=
B
If
A
and
B
are two non-singular matrices, then
A
A
is similar to
B
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B
A
B
is similar to
B
A
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C
A
B
is similar to
A
−
1
B
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D
none of these
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Solution
The correct option is
A
A
B
is similar to
B
A
A
B
=
(
B
−
1
B
)
A
B
=
B
−
1
(
B
A
)
B
∴
A
B
is similar to
B
A
.
Hence, option B.
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