Condition of symmetric matrix

Let A and B are two symmetric 2x2 matrices. Then A=A^T and B=B^T
(AB)^T=(B^T)(A^T)=BA

So, the the condition for obtaining a symmetric matrix by multiplying two symmetric 2x2 matrices is AB=BA. i.e. the multiplication of symmetric matrices is communicative.

Actually, the multiplication of symmetric matrices is communicative. So, The product of two symmetric matrices is also symmetric.