Let the matrix \(\mathrm{A}=\left[\begin{matrix}1 & 0 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0\end{matrix}\right]\) satisfy \({\mat…

Let the matrix \(\mathrm{A}=\left[\begin{matrix}1 & 0 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0\end{matrix}\right]\) satisfy \({\mathrm{A}}^{\mathrm{n}}={\mathrm{A}}^{\mathrm{n}-2}+{\mathrm{A}}^{2}-\mathrm{I}\) for \(\mathrm{n}\geq 3\). Then the sum of all the elements of \({\mathrm{A}}^{50}\) is :-

[JEE Main 2025, 4 Apr (Shift 2)]