Show that for every matrix $A \in M(2 \times 2, \mathbb{C})$ with $A = 0$ or $A^2 \neq 0$ there exists $B \in M(2 \times 2, \mathbb{C})$ with $B^2 = A$.
Normally I would try to write out the matrices in it's components etc, but recently I learned about normal forms and I think there has to be an easier way to prove the statement above.
