Question

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

Answer 1

$\Rightarrow$ A matrix is symmetric if and only if it is equal to its transpose.

$\Rightarrow$ A matrix is skew-symmetric if and only if it is the opposite of its transpose.

$\Rightarrow$ All main diagonal entries of a skew-symmetric matrix are zero.

So, a matrix which satisfied both symmetric and skew-symmetric conditions is a null matrix.

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