Mathematics - Matrices Question with Solution | TestHub

$\begin{array}{rl}& {\mathrm{A}}^{50}={\mathrm{A}}^{48}+{\mathrm{A}}^2-\mathrm{I}\\ & ={\mathrm{A}}^{46}+2\left({\mathrm{A}}^2-\mathrm{I}\right)\\ & ={\mathrm{A}}^{44}+3\left({\mathrm{A}}^2-\mathrm{I}\right)\\ & ={\mathrm{A}}^2+24\left({\mathrm{A}}^2-\mathrm{I}\right)\\ & =25{\mathrm{A}}^2-24\mathrm{I}\end{array}$
$\begin{array}{rl}& =25\left[\begin{array}{lll}1& 0& 0\\ 1& 1& 0\\ 1& 0& 1\end{array}\right]-24\left[\begin{array}{lll}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]\\ & =\left[\begin{array}{ccc}1& 0& 0\\ 25& 1& 0\\ 25& 0& 1\end{array}\right]\end{array}$
Sum $=53$
option (1)