$P$ denote a matrix from set of all $\{0,1\}^{n\times n}$ permutation matrices. We know there is a $k\in\mathbb N$ such that $P^k=I$ the identity.
Given an integer $t\in\mathbb N$ how many $n\times n$ permutations have $P^t=I$?
What is the minimum $t'$ such that all $n\times n$ permutations have $P^{t'}=I$?
What is the smallest $t''>0$ such that every permutation $P$ satisfies $P^{t'''}=I$ at some $1\leq t'''\leq t''$?