If A=(2314)A = \begin{pmatrix} 2 & 3 \\ 1 & 4 \end{pmatrix}A=(2134), what is the relationship between det(A)\det(A)det(A) and det(AT)\det(A^T)det(AT)?
det(A)=det(AT)\det(A) = \det(A^T)det(A)=det(AT)
det(A)=−det(AT)\det(A) = -\det(A^T)det(A)=−det(AT)
det(A)=2⋅det(AT)\det(A) = 2 \cdot \det(A^T)det(A)=2⋅det(AT)
det(AT)=0\det(A^T) = 0det(AT)=0