Math Help - matrix algebra

1. matrix algebra

Let A,B, and C be 2 x 2 matrices with det A=3, det B=-2, and det C=-2012

Compute $det ((-2)A^{T} B^{3} (C^{T})^{-1} A^{-1} (B^{-1})^{2} CA)$

2. Re: matrix algebra

Do you not know that det(AB)= det(A)det(B)? From that it follows that $det(A^n)= (det A)^n$ and, in particular $dA^{-1}= \frac{1}{det(A)}$. Also, it is easy to see that $det(A^T)= det(A)$.