find two matrices A and B such that $A^2 -BA-AB+B^2 = O_{2\times 2}$ Can someone please explain this question to me
Question : Construct a $2\times 2$ matrix A and B with A different from B and neither A = $O_{2\times 2}$ nor $B = O_{2\times 2}$ such that $A^2 - BA - AB + B^2 = O_{2\times 2}$
Attempt: I found a matrix A such such that $a_{11} = 0$, $a_{12} = 0$, $a_{21} =1$, and $a_{22} = 0$ but I couldn't find a second matrix B that will respect the given condition
Thanks.

$A^2 - AB - BA + B^2 = (A-B)^2 = O$
Find a matrix $M$ such that $M^2 = O$ 
How about $M = \begin{pmatrix}0&1\\0&0\end{pmatrix}$
Now find chose $A, B$ such that $(A-B) = M$
