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Question
Mathematics
If A and B are symmetric matrices of the same order, then
Q. If A and B are symmetric matrices of the same order, then
2923
244
Matrices
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A
AB is a symmetric matrix
26%
B
A - B is a skew-symmetric matrix
21%
C
AB + BA is a symmetric matrix
43%
D
AB - BA is a symmetric matrix
9%
Solution:
(
A
B
+
B
A
)
t
=
(
A
B
)
t
+
(
B
A
)
t
=
B
t
A
t
+
A
t
B
t
=
B
A
+
A
B
=
A
B
+
B
A
(
∵
A
t
=
A
and
B
t
=
B
)