A matrix commuting with all matrices from $\mathfrak{sl}(n,\mathbb{R})$ is the zero matrix

Question

Let $\mathfrak{sl}(n,\mathbb{R})=\{X\in\mathfrak{gl}(n,\mathbb{R}): \mathrm{tr}(X)=0\}$ the Lie algebra of $\mathrm{SL}(n,\mathbb{R})$, i want show that, if $X\in\mathfrak{sl}(n,\mathbb{R})$ is such that: $[X,Y]=0$, for all $Y\in\mathfrak{sl}(n,\mathbb{R})$, then: $X=0$. Where, for all $A,B\in\mathfrak{sl}(n,\mathbb{R})$: $$[A,B]=AB-BA.$$ I have no idea how to proceed. Any help would be appreciated!