Nilpotent matrix $A, B$ $\Longrightarrow$ $A+B$ nilpotent.

Nilpotent matrix $A, B$ $\Longrightarrow$ $A+B$ nilpotent.

How to prove that if $A, B$ are matrix of $n\times n$ nilpotents so that
$AB=BA$ then $A+B$ is nilpotent.