Answer
See below
Work Step by Step
$A$ is a $n\times n$ skew- symmetric matrix
then $a_{ij}=a_{ji}$ (according to symmetric property)
and $a_{ij}=-a_{ji}$ (skew-symmetric property)
It follows that $a_{ij}=a_{ji}=-a_{ji}\\
\rightarrow a_{ji}=-a_{ji}$
The only possibility for this kind of matrix is with all zero elements.
Hence, $A$ is a zero matrix.
