Putnam 1969 B6

Let $A$ and $B$ be matrices of size $3\times 2$ and $2\times 3$ respectively. Suppose that $$AB =\begin{pmatrix} 8 & 2 & -2 2 & 5 &4 -2 &4 &5 \end{pmatrix}.$$ Show that the product $BA$ is equal to $\begin{pmatrix} 9 &0 0 &9 \end{pmatrix}.$