Given det(1234)=−2\det \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} = -2det(1324)=−2, what is det(3412)\det \begin{pmatrix} 3 & 4 \\ 1 & 2 \end{pmatrix}det(3142)?
222
−2-2−2
000
111