If \(A\) is a square matrix of order 3 such that \(\operatorname{det}(A)=3\) and \(\operatorname{det}\left(\operatorname…

If \(A\) is a square matrix of order 3 such that \(\operatorname{det}(A)=3\) and \(\operatorname{det}\left(\operatorname{adj}\left(-4 \operatorname{adj}\left(-3 \operatorname{adj}\left(3 \operatorname{adj}\left((2 A )^{-1}\right)\right)\right)\right)\right)=2^{ m } 3^{ n }\), then \(m +2 n\) is equal to :

[JEE Main 2024, 6 Apr (Shift 2)]