Sarrus rules and dihedral groups

TL;DR

This paper analyzes a false generalization of Sarrus' rule using dihedral groups and proposes a Sarrus-like scheme to help students compute 4x4 determinants.

Contribution

It clarifies misconceptions about Sarrus' rule and introduces a new mnemonic scheme for calculating 4x4 determinants based on group theory.

Findings

Identifies the incorrect generalization of Sarrus' rule.

Shows how dihedral groups relate to determinant calculations.

Proposes a new mnemonic scheme for students.

Abstract

This paper is devoted to the analysis of a false generalization of the rule of Sarrus and its properties that can be derived with the help of dihedral groups. Further, we discuss a Sarrus-like scheme that could be helpful for students to memorize the calculation of a $4\times 4$ determinant.