Given a stochastic matrix $P$ representing a Markov chain, I am supposed to find the basis of: $$ \operatorname{Null}(P-I_5) $$
What is this expression supposed to represent and how do I proceed to solve it?
How is this related to the regularity of matrix $P$?
By the Perron-Frobenius theorem and the regularity of $P$, $P^k$ has exactly one eigenvalue of magnitude $1$ for some $k$, and the geometric multiplicity of this eigenvalue is $1$.
We may deduce that the same must also hold for $P$.