Solution:
Consider,
\[\ldots \text{ }\left( i \right)\]
\[\ldots \text{ }\left( ii \right)\]
From (i) and (ii) we can see that
A skew-symmetric matrix is a square matrix whose transpose equal to its negative, that is,
\[X\text{ }=\text{ -}\text{ }{{X}^{T}}\]
So, \[A\text{ }-\text{ }{{A}^{T}}\] is a skew-symmetric.