I am trying to read a solution for this question: Given the following matrix in Jordan form, $$ A= \begin{pmatrix} J_5(0) & \\ & J_6(0) \end{pmatrix} $$ We are asked to find the Jordan form for $A^3$. Now the solution starts with $A$ is 6 nilpotent, because $A^6 = 0$, thus $A^3$ is 2 nilpotent, because $A^6 = (A^3)^2 = 0$, but I don't understand why is it 2 nilpotent and not 1 nilpotent ? Is there something I'm missing ? (The rest of the solution I understand)
Thank you