The matrix $N = \begin{pmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \end{pmatrix}$ is nilpotent. Which of the following statements are true?

(I) All eigenvalues of $N$ are 0. (II) $N$ is diagonalizable. (III) The minimal polynomial of $N$ is $m(\lambda) = \lambda^3$.