Given an $n\times n$ irreducible stochastic matrix $P$, how to prove that ${\rm rank}(I-P)=n-1$?

Question

I want to prove that ${\rm rank}(I-P)=n-1$, and I know that $I-P$ is not full rank, all columns add to be $0$

I want to prove stationary distribution $\pi$ is unique by this so please don't prove it by $\pi$

Any comment will be appreciate!