According to the description here, affine transformation share the same eigenvalues with its linear part, as shown below:

I want to verify this with the symbolic computation of eigenvalues using an affine transformation matrix in Mathematica, however, I find that this calculation will never be completed, as shown below:

Clear[a, b];
mA = Array[a, {3, 3}];
v = Array[b, 3];
aff = AffineTransform[{mA, v}] // TransformationMatrix;
aff // Eigenvalues // FullSimplify[#, Flatten[aff] \[Element] Reals] &

$Aborted

I'm not sure if there's a way to solve this problem with Wolfram language. Any hints will be appreciated.

Regards,
Zhao