1. ## Invertable Matrices

This is a post from alexdudek.

Originally Posted by alexdudek
Suppose A, B, and C are invertible 4x4 dimensional matrices with the properties that det(A)=3, det(B)=5, and det(C)=2. Calculate the determinant of:

(3A^(-1)BCC^(T)A^(3))

I understand matrices and determinants but I can't figure out how to start this question...Could someone help? Once I know how to set it up I think I'd be able to solve it.
Thank you so much.
Thanks
-Dan

2. ## Re: Invertable Matrices

Here are three properties, supposing that A^(-1) is the inverse of A, and C^T is the transpose of C

1) The determinant of a matrix product is equal to the product of the determinants. det(A1A2An)=det(A1)det(A2)det(An)
2) det(A^(-1)) = 1/det(A)
3) det(C^T) = det(C)

EDIT://
also det(cA) = c det(A) for a number c.

3. ## Re: Invertable Matrices

Actually, $\displaystyle \det(cA) = c^n \det(A)$ for an $\displaystyle n\times n$ matrix $\displaystyle A$.