By Tewodros Amdeberhan and Shalosh B. Ekhad (with an appendix by Christoph Koutschan and his computer)
.pdf of article
Written: Oct. 31, 2010.
A pure mathematician called Sheldon Axler once wrote an article called "Down with Determinants!".
We feel sorry for people like him. Evaluating (symbolic) determinants is much more fun than chasing diagrams!
This article uses, among quite a few other methods, a beautiful method described in this
lecture
Personal Journal of Shalosh B. Ekhad and Doron Zeilberger