JEE Math Practice Question

Let the determinant of a square matrix A of order $m$ be $m-n$, where $m$ and $n$ satisfy $4 m+n=22$ and $17 m+4 n=93$. If $\operatorname{det}(n \operatorname{adj}(\operatorname{adj}(m A)))=3^{a} 5^{b} 6^{c}$ then $a+b+c$ is equal to :

1. A.96
2. B.84
3. C.109
4. D.101