Derivative of Inverse Coordinate Transformation

If $\vec{T}(u,v)$ is a 1-1 Differentiable Transformation that maps a region $G$ in the uv-plane to a region $R$ in the xy-plane and $\vec{T}(u_0,v_0)=(x_0,y_0)$, then we have

$$\left|\det (D\vec{T}(u_0,v_0))\right|=\frac{1}{\left|\det (D{\vec{T}}^{-1}(x_0,y_0))\right|}$$