### A Combinatorial Formula for Powers of $3 \times 3$ Matrices and some Combinatorial Identities

*Naraporn Na Chanta, Penying Rochanakul*

#### Abstract

In this paper, we give a closed-form expression for the entries of powers of a $3\times3$ matrix. This formula represents each entries of the power matrix as sum of products of the entires of the original matrix. We derive some combinatorial identities using this formula.

Full Text:

PDF
### Refbacks

- There are currently no refbacks.

**The Thai Journal of Mathematics ***organized and supported by *The Mathematical Association of Thailand and Thailand Research Council and the Center for Promotion of Mathematical Research of Thailand (CEPMART).

**Copyright** 2020 by the Mathematical Association of Thailand.

All rights reserve. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission of the Mathematical Association of Thailand.

|ISSN 1686-0209|