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JEE Main Math Class 12 Matrices Part 1 Questions
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© examsnet.com
Question : 81
Total: 100
Let A and B be any two 3 × 3 matrices. If A is symmetric and B is skewsymmetric, then the matrix AB – BA is:
[Online April 19, 2014]
skewsymmetric
symmetric
neither symmetric nor skewsymmetric
I or – I, where I is an identity matrix
Validate
Solution:
Let A be symmetric matrix and
B
be skew symmetric matrix.
∴
A
T
=
A
and
B
T
=
−
B
Consider
(
A
B
−
B
A
)
T
=
(
A
B
)
T
−
(
B
A
)
T
=
B
T
A
T
−
A
T
B
T
=
(
−
B
)
(
A
)
−
(
A
)
(
−
B
)
=
−
B
A
+
A
B
=
A
B
−
B
A
This shows
A
B
−
B
A
is symmetric matrix.
© examsnet.com
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