Show that there is an $r\in \mathbb{R} $ and a $z\in \mathbb{R} ^{3} $ such that $\left( A-rI_{d} \right) ^{2} \left( z \right) =\begin{bmatrix}0\\0\\0\end{bmatrix}$ but $\left( A-rI_{d} \right)z \neq \begin{bmatrix}0\\0\\0\end{bmatrix}$. Where $$A = \left[\begin{array}{l} 3&-2&2 \\ 4&-4&6 \\ 2&-3&5 \end{array}\right]$$ Matrix $A$ has eigenvalues $\lambda=1,2$ and eigenvectors $\begin{bmatrix}0\\1\\1\end{bmatrix},\begin{bmatrix}1\\2\\1\end{bmatrix}$.
I tried using the eigenvalues a $r$ and the eigenvalues as $z$ but I still can't get it right.