Let A be a matrix of order \(3\times 3\) and \(|A|=5\). If \(|2 \operatorname{adj}(3 \operatorname{Aadj}(2 A))|=2^\alpha…

Let A be a matrix of order \(3\times 3\) and \(|A|=5\). If \(|2 \operatorname{adj}(3 \operatorname{Aadj}(2 A))|=2^\alpha \cdot 3^\beta \cdot 5^{\gamma} \alpha, \beta, \gamma \in N\) then \(\alpha +\beta +\gamma\) is equal to

[JEE Main 2025, 3 Apr (Shift 1)]