Finite-dimensional representations of the integers (2)

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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?