anchor.diff:  
   [stem]
   ++++
  -M^{-1}={\left[ \begin{array}{} A & B \\ C & D \\ \end{array} \right]}^{-1}=\frac{1}{\left|M\right|}{\left[ \begin{array}{} (\left|D\right|A-B(D^{\#}C))^{\#} & (\left|B\right|C-D(A^{\#}B)^{\#})^{\#} \\ (\left|C\right|B-A(D^{\#}C)^{\#})^{\#} & (\left|A\right|D-C(A^{\#}B))^{\#} \\ \end{array} \right]}
  +M^{-1}={\begin{matrix} A & B \\ C & D \\ \end{matrix}}^{-1}=\frac{1}{\left|M\right|}{\begin{matrix} \begin{array}{} (\left|D\right|A-B(D^{\#}C))^{\#} & (\left|B\right|C-D(A^{\#}B)^{\#})^{\#} \\ (\left|C\right|B-A(D^{\#}C)^{\#})^{\#} & (\left|A\right|D-C(A^{\#}B))^{\#} \\ \end{array} \right]}
   ++++
   
   Now it is clear what kind of calculation we need. We need 2x2 matrix multiply and multiply by adjugate: stem:[AB], stem:[A^{\#}B] and stem:[AB^{\#}]. We already know how to do adjugate, but in this case, adjugate can be combined with multiplication so we don’t waste instructions. Just expand the result and rearrange the order, for example:
  
positive.code: 
  [stem]
  ++++
  M^{-1}=\left[ \begin{array}{} \frac{1}{a}\vec{X} & \frac{1}{b}\vec{Y} & \frac{1}{c}\vec{Z} & \vec{0} \\ -\vec{T}\cdot\frac{1}{a}\vec{X} & -\vec{T}\cdot\frac{1}{b}\vec{Y} & -\vec{T}\cdot\frac{1}{c}\vec{Z} & 1 \\ \end{array} \right] = \left[ \begin{array}{} \frac{1}{a}X_0 & \frac{1}{b}Y_0 & \frac{1}{c}Z_0 & 0 \\ \frac{1}{a}X_1 & \frac{1}{b}Y_1 & \frac{1}{c}Z_1 & 0 \\ \frac{1}{a}X_2 & \frac{1}{b}Y_2 & \frac{1}{c}Z_2 & 0 \\ -\vec{T}\cdot\frac{1}{a}\vec{X} & -\vec{T}\cdot\frac{1}{b}\vec{Y} & -\vec{T}\cdot\frac{1}{c}\vec{Z} & 1 \\ \end{array} \right]
  ++++
  
  The nice thing about transform matrix stem:[M] is its first 3 rows are perpendicular to each other. Its inverse form is basically transpose the 3x3 rotation matrix, and rescale it, and change translation part by doing dot product with 3 rescaled axes. It should be easy to confirm stem:[MM^{-1}=I].
  
negative.code: 
  I only listed properties needed for derivation. If you are not familiar with these concepts, or want to know more about them, take a look at the wiki pages above.
  
  Let stem:[M^{-1}={\begin{matrix} A & B \\ C & D \\ \end{matrix}}^{-1}={\begin{matrix} X & Y \\ Z & W \\ \end{matrix}}].Let’s start with the top left corner.
  
  [stem]
  ++++
  