Is there a borel set $A$ and a linear map $f$ such that $f(A)$ is not borel?

Question

Is there a borel set $A\in\mathbb{R}^n$ and a linear map $f:\mathbb{R}^n\to\mathbb{R}^n$ that $f(A)$ is not borel set?

I think there is but I can't find it.

Answer 1

Projection is a linear map and there are Borel subsets of plane that project to non Borel subsets of line.