How can an affine transformation preserve parallelism if it includes an arbitrary nonsingular linear transformation?
Let $A_0$ be a vector, $T$ a nonsingular linear transformation and define an affine transformation of some affine space by $$A \rightarrow A_0 + TA$$
Affine transofmrations are known to preserve parallelism. But how can this be when nonsingular linear transformations need not preserve parallelism? Thanks