For $L=sl\_2(\mathbb{F})$ i.e. matrices with trace zero, what is the centre i.e.  

$Z(L)$= {$x\in L : [x,y]=[y,x] \ \forall\ y \in L$}.

I will have to find matrices $A \in L$ such that $AB=BA$ for all $B \in L$. But how to appoach this considering trace is zero here.