1. please more help with linear algebra

Let A, B, and C be 3x3 invertible matrices where det A = detB = detC

det(-(Atranspose)^2BinverseCinverse) = ?

det[-2(A^2)transposeBtransposeCinverse) = ?

2. Originally Posted by eiktmywib
det(-(Atranspose)^2BinverseCinverse) = ?
I do this one.

$\displaystyle \det (- (A^T)^2 B^{-1} C^{-1}) = (-1)^3 [\det (A^T)]^2 \det (B^{-1})\det (C^{-1})$$\displaystyle = -1 \frac{\det (A) \det (A)}{\det (B) \det (C)} = -1$