Let A be matrix of order 3 × 3. Also let matrices B, C and D are such that B = Adj(A), C = Adj(AdjA), D = (Adj(Adj(AdjA)) if (Adj(Adj(Adj (Adj ABCD)))) is $|\mathrm{A}{|}^{\mathrm{K}}$then K is equal to

$\begin{array}{rcl}\mathrm{B}& =& \mathrm{adjA}, \mathrm{C}=\mathrm{adj}\left(\mathrm{adjA}\right), \mathrm{D}=\mathrm{adj}\left(\mathrm{adj}\right(\mathrm{adjA}\left)\right)\\ & & \left|\mathrm{adj}\left(\mathrm{adj}\right(\mathrm{adj}\left(\mathrm{adj}\right(\mathrm{ABCD}\left)\right)\left)\right)\right|\\ \mathrm{ABCD}& =& \mathrm{E}\\ & & \left|\mathrm{adj}\left(\mathrm{adj}\right(\mathrm{adj}\left(\mathrm{adJE}\right)\left)\right)\right|\\ & =& {\left|\mathrm{E}\right|}^{{(4-1)}^4}=|\mathrm{E}{|}^{16}\\ & =& |\mathrm{ABCD}{|}^{16}\\ & =& |\mathrm{A}{|}^{16} |\mathrm{B}{|}^{16} |\mathrm{C}{|}^{16} |\mathrm{D}{|}^{16}\\ & =& |\mathrm{A}{|}^{16} {\left({\left|\mathrm{A}\right|}^{3-1}\right)}^{16} {\left({\left|\mathrm{A}\right|}^{{(3-1)}^2}\right)}^{16} {\left({\left|\mathrm{A}\right|}^{{(3-1)}^3}\right)}^{16}\\ & =& |\mathrm{A}{|}^{16} |\mathrm{A}{|}^{32} |\mathrm{A}{|}^{64} |\mathrm{A}{|}^{128}\\ & =& |\mathrm{A}{|}^{16+32+64+128}\\ & =& |\mathrm{A}{|}^{240}\end{array}$