Mathematics - Matrices Question with Solution | TestHub

$|(\det (\mathrm{A}))\mathrm{adj}(5\mathrm{adj}(\mathrm{A}))|$ $=\left|2\mathrm{adj}\left(5\mathrm{adj}\left({\mathrm{A}}^3\right)\right)\right|$ $=2^3\mid \mathrm{adj}(5\mathrm{adj}\left({\mathrm{A}}^3\right)\Vert$ $=2^3\cdot {\left|5\mathrm{adj}\left({\mathrm{A}}^3\right)\right|}^2$ $=2^3{\left(5^3\cdot \left|\mathrm{adj}\left({\mathrm{A}}^3\right)\right|\right)}^2$ $=2^3\cdot 5^6\cdot {\left|\mathrm{adj}{\mathrm{A}}^3\right|}^2$ $=2^3\cdot 5^6{\left({\left(|\mathrm{A}{|}^3\right)}^2\right)}^2$ $=2^3\cdot 5^6\cdot 2^{12}=2^{15}\times 5^6$ $=2^9\times 10^6$ $=512\times 10^6$