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JEE Advanced Model Paper 2 with solutions for online practice
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© examsnet.com
Question : 37
Total: 54
If A and B are symmetric non singular matrices such that AB = BA and
A
−
1
B
−
1
exists then
A
−
1
B
is symmetric
A
B
−
1
is symmetric
A
−
1
B
−
1
is symmetric
A
−
1
B
−
1
is skew symmetric
Validate
Solution:
(
A
−
1
B
)
T
=
B
T
(
A
−
1
)
T
=
B
T
(
A
T
)
−
1
=
B
A
−
1
=
A
−
1
A
B
A
−
1
=
A
−
1
B
A
A
−
1
=
A
−
1
B
∴
A
−
1
B
is symmetric
∴ here (a) is true, similarly (b) is true
(
A
−
1
B
−
1
)
T
=
(
B
−
1
)
T
(
A
−
1
)
T
=
(
B
T
)
−
1
(
A
T
)
−
1
=
B
−
1
A
−
1
=
(
A
B
)
−
1
=
(
B
A
)
−
1
=
A
−
1
B
−
1
Here ( c) is correct
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