I was reading the answer of the question from this link:
Finite-dimensional representations of the integers
But I have 2 things that I do not understand in the solution and the comments of the above link:
1- In case of $\mathbb{Z}$, why every invertible matrix will work?
2- why for a faithful representation $\rho (1) =2I$ will work?
Could anyone explain this for me please?