Finding matrix BA given AB 
Given a matrix $$AB = \begin{bmatrix}-2&-14&14\\5&15&-10\\4&8&-3\end{bmatrix},$$ where $A$ is a $3\times 2$ matrix, and $B$ a $2\times 3$ matrix, how do I find the matrix $BA$?

I was told to find the basis for the rowspace of $AB$, and that $(AB)^2 = 5AB$. However, I do not see how these 2 informations can help me find $BA$ at all.
Any help would be appreciated.

We have that $\mbox{rank}(AB)=2$ and 
$$5AB=(AB)^2 \Rightarrow 0=(AB)^2-5(AB)=A(BA-5I_2)B.$$
Now show that $BA=5I_2$ (but be careful because $A$ and $B$ are not square matrices).
