If $\mathrm{A}=\left[\begin{array}{cc}0& \mathrm{\alpha }\\ 0& 0\end{array}\right]$ and ${\left(\mathrm{A}+\mathrm{I}\right)}^{50}-50\mathrm{A}=\left[\begin{array}{cc}\mathrm{a}& \mathrm{b}\\ \mathrm{c}& \mathrm{d}\end{array}\right]$ , 

the value of a + b + c + d is

$$\begin{gathered} \mathrm{A}=\left[\begin{array}{cc}0& \mathrm{\alpha }\\ 0& 0\end{array}\right] \\ \Rightarrow A+I=\left[\begin{array}{cc}1& \mathrm{\alpha }\\ 0& 1\end{array}\right]\Rightarrow {\left(A+I\right)}^2=\left[\begin{array}{cc}1& \mathrm{\alpha }\\ 0& 1\end{array}\right]\left[\begin{array}{cc}1& \mathrm{\alpha }\\ 0& 1\end{array}\right]=\left[\begin{array}{cc}1& 2\mathrm{\alpha }\\ 0& 1\end{array}\right] \\ {\left(A+I\right)}^{50}=\left[\begin{array}{cc}1& 50\mathrm{\alpha }\\ 0& 1\end{array}\right]\Rightarrow {\left(A+I\right)}^{50}-50A=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]=\left[\begin{array}{cc}a& b\\ c& d\end{array}\right] \\ a+b+c+d=2 \end{gathered}$$