Sum of two skew-symmetric matrices is always………matrix.

Let A is a given matrix, then $$\left( { - A} \right)$$ is a skew-symmetric matrix.

Similarly, for a given matrix $$ - B$$ is a skew-symmetric matrix.

Hence, $- A - B = - (A + B)$ $\Rightarrow$ sum of two skew-symmetric matrices is always skew-symmetric matrix.