Mathematics - Matrices Question with Solution | TestHub

$\begin{array}{rl}& |\mathrm{A}|=3\\ & \mid \mathrm{adj}(-4\mathrm{adj}\left(-3\mathrm{adj}\left(3\mathrm{adj}\left((2\mathrm{A}{)}^{-1}\right)\right)\right)\mid \\ & \mid -4\mathrm{adj}(-{3\mathrm{adj}\left(3\mathrm{adj}(2\mathrm{A}{)}^{-1}\right)|}^2\\ & 4^6{\left|\mathrm{adj}\left(-3\mathrm{adj}\left(3\mathrm{adj}(2\mathrm{A}{)}^{-1}\right)\right)\right|}^2\\ & 2^{12}\cdot 3^{12}{\left|3\mathrm{adj}(2\mathrm{A}{)}^{-1}\right|}^8\\ & 2^{12}\cdot 3^{12}\cdot 3^{24}{\left|\mathrm{adj}(2\mathrm{A}{)}^{-1}\right|}^8\end{array}$ $\begin{array}{rl}& 2^{12}\cdot 3^{36}{\left|(2\mathrm{A}{)}^{-1}\right|}^{16}\\ & 2^{12}\cdot 3^{36}\frac{1}{|2\mathrm{A}{|}^{16}}\\ & 2^{12}\cdot 3^{36}\frac{1}{2^{48}|\mathrm{A}{|}^{16}}\\ & 2^{12}\cdot 3^{36}\frac{1}{2^{48}\cdot 3^{16}}\\ & \frac{3^{20}}{2^{36}}=2^{-36}\cdot 3^{20}\\ & \mathrm{m}=-36\mathrm{n}=20\\ & \mathrm{m}+2\mathrm{n}=4\end{array}$