How to transform a matrix into a fixed point form

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As asked in the title, how to transform a $3 × 3$ matrix into the fixed point form $x=Tx+b$?

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Hint: Observe \begin{align} Ax=b \ \ \Rightarrow \ \ (D+N)x = b \end{align} where $D$ is the diagonal of $A$ and $N$ is everything else. Then it follows \begin{align} x = D^{-1}b - D^{-1}Nx. \end{align} This is called the Jacobi fixed-point form.