MathDB

Let

A

be a square matrix with entries in the field

\mathbb Z / p \mathbb Z

such that

A^n - I

is invertible for every positive integer

n

. Prove that there exists a positive integer

m

such that

A^m = 0

.
(A matrix having entries in the field

\mathbb Z / p \mathbb Z

means that two matrices are considered the same if each pair of corresponding entries differ by a multiple of

p

.)
Proposed by Tony Wang

Problem Statement