Let \(A=\left[\begin{matrix}2 & 2+p & 2+p+q \\ 4 & 6+2p & 8+3p+2q \\ 6 & 12+3p & 20+6p+3q\end{matrix}\right]\). If \(\de…

Let \(A=\left[\begin{matrix}2 & 2+p & 2+p+q \\ 4 & 6+2p & 8+3p+2q \\ 6 & 12+3p & 20+6p+3q\end{matrix}\right]\).
If \(\det (adj(adj(3\mathrm{A})))={2}^{\mathrm{m}}\cdot {3}^{\mathrm{n}},\mathrm{m},\mathrm{n}\in \mathrm{ℕ}\), then \(\mathrm{m}+\mathrm{n}\) is equal to

[JEE Main 2025, 8 Apr (Shift 1)]