A combinatorial proof of Cramer's Rule

By Doron Zeilberger


.pdf     .tex
Exclusively published in the Personal Journal of Shalosh B. Ekhad and Doron Zeilberger and arxiv.org

Written: Aug. 18, 2024


In honor of my Rutgers colleague, Antoni A. Kosinski (b. 1930), who proved that Cramer's Rule is indeed due to Cramer.


In 1750, Gabriel Cramer famously stated, without proof, his eponymous rule for solving a system of linear equations with as many equations as unknowns. We give a purely combinatorial, and purely self-contained, proof of this old chestnut, still useful after all these years.

Added Aug. 21, 2024: Thanks to Alex Heaton for correcting typos in the previous version.

Maple package


Personal Journal of Shalosh B. Ekhad and Zeilberger