The diagonal entries of any skew-symmetric matrix are:

A skew-symmetric matrix satisfies $a_{ij} = -a_{ji}$ for all $i, j$. Setting $i = j$ gives $a_{ii} = -a_{ii}$, hence $2a_{ii} = 0$, so $a_{ii} = 0$. Every diagonal entry of a skew-symmetric matrix is therefore zero.