IMC 2004 Problem 7

Let $A$ be a real $4\times 2$ matrix and $B$ be a real $2\times 4$ matrix such that $$AB = \left(\begin{array}{cccc} 1 & 0 & -1 & 0 0 & 1 & 0 & -1 -1 & 0 & 1 & 0 0 & -1 & 0 & 1 \end{array}\right).$$ Find $BA$ .