Help with determinant calculation

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• Jul 17th 2013, 02:54 AM
ggaston
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?
• Jul 17th 2013, 06:22 AM
HallsofIvy
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.
• Jul 17th 2013, 07:43 AM
ggaston
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
• Jul 18th 2013, 03:02 AM
Prove It
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...