Constructing two matrices that do not commute I need to construct square matrices $A$ and $B$ such that $AB=0$ but $BA \neq 0$. 
I know matrix multiplication is not commutative, but I don't know how to construct such matrices. Thanks in advance.
Edit: looking for some simple way

Yet another more powerful (and maybe more "advanced"):
Let A be a given matrix, now $AB-BA$ can be rewritten with help of matrix multiplication and vectorization as: $M_{AR}\text{vec}(B) - M_{AL}\text{vec}(B)$, where $M_{AR}$ is a matrix performing multiplication from the Right by $A$ and $M_{AL}$ from Left by $A$.
We can now first pick a vectorization $\text{vec}$ and an objective matrix $C$ and try to solve $$\min_B\{\|(M_{AR}-M_{AL})\text{vec}(B)-\text{vec}(C)\|\}$$
Where $C = AB-BA$ is something we can choose.
