Solution
= Solution
The inverse <derivative> formula, evaluated at $G(0,0)=(0,0)$, gives
$$
\boxed{D(G^{-1})(0,0)=\begin{pmatrix}1&1\\1&0\end{pmatrix}^{-1}=\begin{pmatrix}0&1\\1&-1\end{pmatrix}.}
$$
Multiplying the two displayed <matrices> in either order gives the <identity element>, verifying the <total derivative> explicitly.