$A$ and $B$ are skew-symmetric matrices of the same order. What is $A + B$ always?

Explanation

1. 01

   $(A + B)' = A' + B' = -A - B = -(A + B)$.

2. 02

   So $A + B$ is skew-symmetric. The same steps show that $A - B$ and $kA$ are skew-symmetric too.