If the determinant of the matrix A is 3 then what is the determinant of det(4A)?
The answer involves something like this:
$\displaystyle 4^2det(A)$
why does 4 get squared and come out in front?
Basic properties of determinants, and it is $\displaystyle 4^2$ only if the matrix is 2 x 2; in general, if the determinant is n x n, $\displaystyle \det (kA)=k^n\det A\,,\,\,k$ a scalar.