Past exam of the mathematics course of the University of Oxford / 2017 / Prelims / Mathematics II / 1 / b / iv / Solution

False. Take $x_{1,n}=0$ for every $n$, and $x_{m,n}=1$ for every $m\ge 2$ and every $n$. Each row is constant, so its infimum and supremum coincide. Nevertheless,The two outer extrema can select different rows.