## Find a generating matrix of a finite field

Hi there

I am trying to solve this exercise:

Find $M \in \mathbb{F}_7^3$ such that $\forall x,y \in \mathbb{F}_7^3 \setminus \{0\} \exists m$ such that $M^m*x=y$

So I searched for a generating Matrix that has full rank? But when trying $\Big( \begin{matrix}2 & 3 & 5 \\3 & 5 & 2 \\5 & 2 & 3 \end {matrix} \Big)$ I couldn't prove that this is a bijection allthough it has full rank and all the numbers do not divide 7??

Do you know the way finding such a matrix here?