Let\(\mathrm{A}=\left[{\mathrm{a}}_{\mathrm{ij}}\right]=\left[\begin{matrix}{\log }_{5}128 & {\log }_{4}5 \\ {\log }_{5}…

Let\(\mathrm{A}=\left[{\mathrm{a}}_{\mathrm{ij}}\right]=\left[\begin{matrix}{\log }_{5}128 & {\log }_{4}5 \\ {\log }_{5}8 & {\log }_{4}25\end{matrix}\right].\) If \({\mathrm{A}}_{\mathrm{ij}}\) is the cofactor of \({\mathrm{a}}_{\mathrm{ij}},{\mathrm{C}}_{\mathrm{ij}}=\sum _{\mathrm{k}=1}^{2}{\mathrm{a}}_{\mathrm{ik}}{\mathrm{A}}_{\mathrm{jk}},1\leq \mathrm{i},\mathrm{j}\leq 2,\), and \(\mathrm{C}=\left[{\mathrm{C}}_{\mathrm{ij}}\right]\), then \(8|\mathrm{C}|\) is equal to :

[JEE Main 2025, 29 Jan (Shift 1)]