If A is non-singular matrix of order $4\times 4$ and determinant of $Adj(A) = 4$, then the value of $\left | 2 Adj(3A) \right |$ is ?
To solve this question I began with the knowledge that $$\ \left | Adj(kA)\right | = k^{n(n-1)}\ \ \left | A \right |^{n-1} \ \ where\ n\ is\ the\ order\ of\ the\ square\ matrix \ $$
$$ \ \ \ \ ( \ \left | Adj(A)\right | = \left | A \right |^{n-1} \ )$$
Therefore $$\left | Adj(3A)\right | = 3^{4*3} \ \left | A \right |^{3} $$
Now when taking a scalar term outside a determinant, it is raised to the power of the order of the matrix.
So in our case $ \ \left | 2Adj(3A)\right | = 2^{4} \ 3^{12} \ 4^{3} $
Is my solution correct?
Edit: My answer above is not correct lol
I had equated $ \left | A \right | = 4 \ $ instead of $ \ \left | Adj(A)\right | = 4 \ $ as mentioned by @Semiclassical.
So the answer actually comes up to $ 2^{6} * 3^{12}$