$A = \begin{bmatrix} 0 & 5 & 1 \\ p & 0 & -3 \\ q & r & 0 \end{bmatrix}$ is skew-symmetric. Find $p + q + r$.

Explanation

1. 01

   In a skew-symmetric matrix $a_{ji} = -a_{ij}$.

2. 02

   So $p = -5$, $q = -1$ and $r = 3$, and $p + q + r = -3$.