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

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

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- Nov 12th 2012, 04:13 PMdumbledorematrix algebra
Let A,B, and C be 2 x 2 matrices with det A=3, det B=-2, and det C=-2012

Compute $\displaystyle det ((-2)A^{T} B^{3} (C^{T})^{-1} A^{-1} (B^{-1})^{2} CA)$ - Nov 12th 2012, 04:48 PMHallsofIvyRe: matrix algebra
Do you not know that det(AB)= det(A)det(B)? From that it follows that $\displaystyle det(A^n)= (det A)^n$ and, in particular $\displaystyle dA^{-1}= \frac{1}{det(A)}$. Also, it is easy to see that $\displaystyle det(A^T)= det(A)$.