$Y=\left[\begin{array}{ccc} \alpha & \beta & \gamma \\ 0 & \alpha & \beta \\ 0 & 0 & \alpha \end{array}\right], Z=\left[\begin{array}{ccc} \alpha^{2} & -\alpha \beta & \beta^{2}-\alpha \gamma \\ 0 & \alpha^{2} & -\alpha \beta \\ 0 & 0 & \alpha^{2} \end{array}\right]$

$Y \cdot Y^{-1}=I$

${\left[\begin{array}{lll}\alpha & \beta & \gamma \\ 0 & \alpha & \beta \\ 0 & 0 & \alpha\end{array}\right]\left[\begin{array}{ccc}\frac{1}{5} & \frac{-2}{5} & \frac{1}{5} \\ 0 & \frac{1}{5} & \frac{-2}{5} \\ 0 & 0 & \frac{1}{5}\end{array}\right]=\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right] }$

$\frac{\alpha}{5}=1 \Rightarrow \alpha=5$

$-\frac{2}{5} \alpha+\frac{\beta}{5}=0 \Rightarrow \beta=10$

$\frac{\alpha}{5}-\frac{2 \beta}{5}+\frac{\gamma}{5}=0 \Rightarrow \gamma=15$

$\Rightarrow(\alpha-\beta+\gamma)^{2}=(5-10+15)^{2}=100$