$A = [a_{ij}]$ is a 3 × 3 matrix with $a_{ij} = i - j$ when $i < j$ and $a_{ij} = i + j$ when $i \ge j$. What is $a_{13} + a_{31}$?

Explanation

1. 01

   For $a_{13}$, $i = 1 < j = 3$, so $a_{13} = 1 - 3 = -2$.

2. 02

   For $a_{31}$, $i = 3 \ge j = 1$, so $a_{31} = 3 + 1 = 4$.

3. 03

   The sum is $-2 + 4 = 2$.