16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 5.3.13

Determinants

Mathematics — Linear Algebra · sign-function-permutations

Problem

Prove that the sign function on permutations is unique in the following sense. If ff is any function which assigns to each permutation of degree nn an integer, and if f(στ)=f(σ)f(τ)f(\sigma\tau) = f(\sigma)f(\tau), then ff is identically 00, or ff is identically 11, or ff is the sign function.

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