I need help this question
Prove that every finite ring has the Invariant Dimension Property (IDP). (Assume $1_R \neq 0_R$.)
This is what I know I should do. Let $X$ and $Y$ be two sets such that the free module with basis $X$ is isomorphic to the free module with basis $Y$. Next, I have to show that $|X| = |Y|$. This is where I'm stuck.
Thanks.