Affine transformation rules - Revisited

Following yesterday's post here are the 'five rules' which aren't rules in Mathematica. Basically there is only one rule where the affine transformation consisting of invertible matrix $A$ and vector $t$ are mapped to a 3-by-3 matrix after which composition of affine transformations ( including translations only ) can be done by multiplying matrices.


f[A_, t_] := ArrayFlatten[{{A, Transpose[{t}]}, {0, 1}}]

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