Let the determinant of a square matrix A of order m be m - n, where m and n satisfy 4m + n = 22 and 17m + 4n = 93 if det (n adj (adj (mA))) = 3^a5^b6^c then a + b + c =

4m + n = 22 and 17m + 4n = 93
From given equations m = 5, n = 2 
$\left|A\right|=3$
det (n adj (adj (mA)))
$$\begin{gathered} \begin{array}{l}=|2\mathrm{Adj}(\mathrm{Adj}5\mathrm{A}\left)\right| \\ =2^5\left|5^{16}\mathrm{Adj}\left(\mathrm{AdjA}\right)\right| \\ =2^5{\left(5^{16}\right)}^5|\mathrm{A}{|}^{4^2}\\ =3^{11}{5}^{80}{6}^5 \\ =3^{\mathrm{a}}{5}^{\mathrm{b}}{6}^{\mathrm{c}}. \\ \Rightarrow \mathrm{a}=11,\mathrm{b}=80,\mathrm{c}=5 \\ \Rightarrow \mathrm{a}+\mathrm{b}+\mathrm{c}=96\end{array} \end{gathered}$$