$A$ is a $3\times3$ matrix and $A^2+4 A−12 I =0 $. If det$(A+2I )>0$, what is $det(A+2I )$? I need to rearrange the following $A^2+4A-12I=0$, where $A$ is an unknown $3\times3$ matrix so that I can find det of $(A+2I)$

A has -6 and 2 and 0 as Eigen values. It can be a matrix with all elements zero except diagonal matrix with -6,2,0 in the diagonal. Now the determinant of A+2I should be greater than zero and it will be if 2 is at 1,1 and -6 at 3,3.
This matrix satisfies all the conditions u asked. And determinant of A+2I is 4. Not the best method though.
