$\begin{bmatrix}0 & a - 2 & 3 \\ 1 & 0 & b + 1 \\ -3 & 4 & 0\end{bmatrix}$ is skew-symmetric. What is $a + b$?

Explanation

1. 01

   $a_{12} = -a_{21}$: $a - 2 = -1$, so $a = 1$.

2. 02

   $a_{23} = -a_{32}$: $b + 1 = -4$, so $b = -5$. Then $a + b = -4$.