Answer
True
Work Step by Step
The given statement is a part of Definition 7.6.1.
If $p$ is the smallest positive integer such that $(A − λI)p v = 0$, then the vector $(A − λI)^{p−1}v$ is a (regular) eigenvector of $A$ corresponding to $λ$, since it belongs to the null space of $A − λI$.