I would want to make an example of a matrix $M \in GL_3(\mathbb{Z}_7)$ such that $\langle M; +, \cdot \rangle \simeq GF(7^3)$ and the multiplicative order of $M$ is $3$.
Any hints how to do that with a computer algebra system would be appreciated.
I would want to make an example of a matrix $M \in GL_3(\mathbb{Z}_7)$ such that $\langle M; +, \cdot \rangle \simeq GF(7^3)$ and the multiplicative order of $M$ is $3$.
Any hints how to do that with a computer algebra system would be appreciated.