Let A be a matrix of order 3× 3 and det(A)=2. Then det(det(A)adj(5adj(A^3)) is equal to .

$|(\operatorname{det}(\mathrm{A})) \operatorname{adj}(5 \operatorname{adj}(\mathrm{A}))|$∣(det(A))adj(5adj(A))∣ $=\left|2 \operatorname{adj}\left(5 \operatorname{adj}\left(\mathrm{A}^3\right)\right)\right|$=​2adj(5adj(A3))​ $=2^3 \mid \operatorname{adj}\left(5 \operatorname{adj}\left(\mathrm{A}^3\right) \|\right.$=23∣adj(5adj(A3)∥ $=2^3 \cdot\left|5 \operatorname{adj}\left(\mathrm{A}^3\right)\right|^2$=23⋅​5adj(A3)​2 $=2^3\left(5^3 \cdot\left|\operatorname{adj}\left(\mathrm{A}^3\right)\right|\right)^2$=23(53⋅​adj(A3)​)2 $=2^3 \cdot 5^6 \cdot\left|\operatorname{adj} \mathrm{A}^3\right|^2$=23⋅56⋅​adjA3​2 $=2^3 \cdot 5^6\left(\left(|\mathrm{~A}|^3\right)^2\right)^2$=23⋅56((∣ A∣3)2)2 $=2^3 \cdot 5^6 \cdot 2^{12}=2^{15} \times 5^6$=23⋅56⋅212=215×56 $=2^9 \times 10^6$=29×106 $=512 \times 10^6$=512×106