For a \(3 \times 3\) matrix \(M\) , let trace \((\mathrm{M})\) denote the sum of all the diagonal elements of \(M\) . Le…

For a \(3 \times 3\) matrix \(M\) , let trace \((\mathrm{M})\) denote the sum of all the diagonal elements of \(M\) . Let \(A\) be a \(3 \times 3\) matrix such that \(|A|=\frac{1}{2}\) and trace \((A)=3\). If \(B=\operatorname{adj}(\operatorname{adj}(2 A))\), then the value of \(|B|+\operatorname{trace}(B)\) equals:

[JEE Main 2025, 22 Jan (Shift 2)]