Question

If a matrix is invertible is it necessarily "one-to-one"?

Answer 1

A matrix cannot be "one-to-one".

Explanation:

I think you are asking if a function (often represented by matrices) is invertible, is it necessarily "one-to-one" (injective)?

The answer is yes. A function is bijective (invertible) if and only if it is injective and surjective (one-to-one and onto).

https://en.wikipedia.org/wiki/Bijection,_injection_and_surjection