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### Computing $\mathbb{C}[x,y]^G$ or $\mathbb{C}[x,y,z]^G$ where $G$ is a finite subgroup of $GL_n(\mathbb{C})$

My question is related to this link: Ring of Invariant $\mathbf{Question \;1}$. Let $$A = \left( \begin{array}{cc} 0 & -1 \\ 1& 0 \\ \end{array} \right).$$ Then $C= \langle A\rangle$ ...
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