Write a 2 × 2 matrix which is both symmetric and skew-symmetric.
Question:

Write a $2 \times 2$ matrix which is both symmetric and skew-symmetric.

Solution:

A matrix which is both symmetric and skew-symmetric is a null matrix.

Hence, the required matrix is $\left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right]$.