# Does a symmetric matrix $A^2$ imply a symmetric $A$?

Does a symmetric matrix $A^2$ imply a symmetric $A$?

Any help would be much appreciated.

No. $$\left( \begin{array}{cc} 0 & 1 \\ 2 & 0 \end{array} \right) \left( \begin{array}{cc} 0 & 1 \\ 2 & 0 \end{array} \right) = \left( \begin{array}{cc} 2 & 0 \\ 0 & 2 \end{array} \right)$$ which is symmetric.
No, for instance take $A$ antisymmetric.