A and B are symmetric matrices
A=A'$\rightarrow$ transpose of A
B=B'$\rightarrow$ transpose of B
Now consider AB-BA
Taking transpose of it we get
From the property of transpose of a matrix we have (AB)'=B'A'.
Replacing A'=A and B'=B(Since A and B are symmetric matrix)
=BA-AB=-(AB-BA)( By taking out -1)
AB-BA is a skew symmetric matrix.
so (A) is the right option.