Help with determinant calculation

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?

Re: Help with determinant calculation

"I don't even know if I is the inverse of A or just another random matrix."

Seriously? Obviously I is NOT "the inverse of A" because that is already represented as A^-1. I is the **standard** notation for the identity matrix.

Re: Help with determinant calculation

Quote:

Originally Posted by

**HallsofIvy** "I don't even know if I is the inverse of A or just another random matrix."

Seriously? Obviously I is NOT "the inverse of A" because that is already represented as A^-1. I is the **standard** notation for the identity matrix.

I mean the identity matrix, I was thinking about other thing

Re: Help with determinant calculation

Quote:

Originally Posted by

**ggaston** 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?

Expand out your expression and then apply the properties of determinants...