proving equation of an invertible matrix as far as i can tell the following sentence is true but what are the steps to actually prove it?
If A is Invertable matrix, and AX=B, then every Y!=X will have AY != B.

by logic it seems this sentence is true, but how can I prove it? what are the steps of a proof?

Suppose that $$AX=B=AY,$$then $$A(X-Y)=0.$$ Now multiply by $A^{-1}$ and conclude.
