If $A^2 =0$ then possible rank of $A$ 
Let, $A$ be a non zero matrix of order $8$ with $A^2 =0.$ Then one of the possible value for rank of $A$ is
(a) $5$ (b) $4$ (c) $6$  (d) $8$.

Attempt :
As , $A^2=0$ , so $A$ is a nilpotent matrix of order $2$. So , characteristic polynomial of $A$ is of the form $x^2f(x)$ , where $f(x)$ is a polynomial of degree $6$. So , possible values of $rank(A)$ are $4,5,6$.
Am I correct ?

Hint: Since $A^2 = 0$, what can you say about the null space and range of $A$?
