I've got this problem:

Let A be a 3x3 matrix. The determinant of A is 1/2 and det[(3A^2+3A+3I)(2A-2I)] =432

Then det[A^-1(A^3-I)^3 A^-1] is : A)32 B)2 C)4*72^3 D)4*7^3 E)-7/2?

I know the rules for determinants, for this problem is far more complex, I don't even know if I is the inverse of A or just another random matrix.

How do you solve this?