Let A be a matrix of order 3 × 3 and det(A) = 2 . Then det(det ( A...

(|(\operatorname{det}($\mathrm{A})) \operatorname{adj}($5 \operatorname{adj}($\mathrm{A}))|$) (=\left|2 \operatorname{adj}\left(5 \operatorname{adj}\left(\mathrm{A}^3\right)\right)\right|) (=2^3 \mid \operatorname{adj}\left(5 \operatorname{adj}\left(\mathrm{A}^3\right) \|\right.) (=2^3\cdot\left|5 \operatorname{adj}\left(\mathrm{A}^3\right)\right|^2) (=2^3\left(5^3 \cdot\left|\operatorname{adj}\left(\mathrm{A}^3\right)\right|\right)^2) (=2^3 $\cdot$5^6 \cdot\left|\operatorname{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$10^6) (=512$\times10^6)