Write a square matrix which is both symmetric as well as skew-symmetric.

Let $A=\left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right]$

$A^{T}=\left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right]$

Since $A^{T}=A, A$ is a symmmetric matrix.

Now,

$-A=-\left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right]$

$\Rightarrow-A=\left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right]$

Since $A^{T}=-A, A$ is $a$ skew $-$ symmetric matrix.

Thus, $A=\left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right]$ is an example of a matrix that is both symmetric and skew-symmetric.