Let $A$ be a C*-algebra. Show that there is $x\in A$ such that $x^2=0$.
I think in abelian C*-algebra $x^2=0$ if and only if $x=0$(because these elements are continuous functions) Also in certain C*-algebras such as $M_2(\Bbb C)$, I can find this element, but I can not show it in general. Please just give me a hint for that. Thanks.