Dimension of algebraic group and morphism

Question

Let $G$ and $G'$ be two affine connected algebraic groups. Let $f: G\rightarrow G'$ be an epimorphisme, etale and finite morphism of algebraic groups. Why do we have $dim(G)=dim(G')$?

Answer 1

This has nothing to do with algebraic groups. Namely, if $f:X\to Y$ is a surjective integral morphism of schemes then $\dim(X)=\dim(Y)$. One can check this by quickly reducing to the affine case, and then using the going-up theorem. For details you can see [1, Tag0ECG].

[1] Various authors, 2020. Stacks project. https://stacks.math.columbia.edu/