NL-NWO 1966 Problem 4

A rectangular piece of paper is divided into square cells by lines parallel to the sides of the rectangle. $n$ (horizontal) rows of $m$ cells have emerged and $m$ (vertical) columns of $n$ cells have also been formed. There is a number in each cell. Find the largest number in each of the $n$ rows. The smallest maxima of those $n$ rows is called $A$ . We also look for the smallest number in each of the $m$ columns. The largest minima of those $m$ columns is called $B$ . Prove that $A$ is greater than or equal to $B$ . Can you give a simple example where $A = B$ ?