Mathematics - Matrices Question with Solution | TestHub

$\begin{array}{rl}& |2\mathrm{adj}(3\mathrm{A}\mathrm{adj}(2\mathrm{A}))|\\ & 2^3\cdot |3\mathrm{A}\mathrm{adj}(2\mathrm{A}){|}^2\\ & 2^3\cdot {\left(3^3\right)}^2\cdot |\mathrm{A}{|}^2\cdot |\mathrm{adj}(2\mathrm{A}){|}^2\\ & 2^3\cdot 3^6\cdot |\mathrm{A}{|}^2\cdot {\left(|2\mathrm{A}{|}^2\right)}^2\\ & 2^3\cdot 3^6\cdot |\mathrm{A}{|}^2{\left[{\left(2^3\right)}^2\cdot |\mathrm{A}{|}^2\right]}^2\\ & 2^3\cdot 3^6\cdot |\mathrm{A}{|}^2\cdot 2^{12}\cdot |\mathrm{A}{|}^4\\ & 2^{15}\cdot 3^6\cdot |\mathrm{A}{|}^6\\ & 2^{15}\cdot 3^6\cdot 5^6=2^{\alpha }\cdot 3^{\beta }\cdot 5^{\gamma }\\ & \alpha =15,\beta =6,\gamma =6\\ & \alpha +\beta +\gamma =27\end{array}$