Question 2
The $n^2$ numbers $\mathbf{x}_{ij}$ satisfy the $n^3$ equations: $\mathbf{x}_{ij} + \mathbf{x}_{jk} + \mathbf{x}_{ki} = 0$. Prove that we can find numbers $\mathbf{a}_1, \ldots, \mathbf{a}_n$ such that $\mathbf{x}_{ij} = \mathbf{a}_i - \mathbf{a}_j$.