# Where to begin when comparing matrices and their inverses

I've just started with linear algebra and am NOT looking for the answer. I'm just looking for a way to begin answering the following true/false question:

If A,B,C are matrices of the same size such that A+C=B+C then A=B and A(−1) =B(−1)

The A(-1) and B(-1) are the inverses of A and B.

Should I create, let's say, a 2x2 matrix (with any numbers) for A, B, and C?

If so, then what would be my next step?

Looking at e.g. the $2\times 2$ case may give an intuition whether a statement is wrong or false and might even give an idea how to prove/disprove the statement rigorously. Nevertheless, this does not give a proof.
How would you proceed in case that $A,B,C$ would not be matrices but, let us say real numbers?
And moreover, why can we even say what the inverse of the matrix $A$ is?