Welcome to mathimatikoi.org forum; Enjoy your visit here.

## Matrices!

Linear Algebra
Riemann
Articles: 0
Posts: 170
Joined: Sat Nov 14, 2015 6:32 am
Location: Melbourne, Australia

### Matrices!

Let $p$ be a prime and let $\mathbb{F}_p=\mathbb{Z} / p \mathbb{Z}$. Find all $p \times p$ matrices $A$ and $B$ over $\mathbb{F}_p$ such that $AB - BA = \mathbb{I}$.

Question: Can you do that in characheristic zero or for $n \times n$ matrices where $p$ does not divide $n$ ? Give a brief explanation.
$\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^s}= \prod_{p \; \text{prime}}\frac{1}{1-p^{-s}}$

Tags: