Kunze Linear Algebra · Problem 5.3.4

Determinants

Mathematics — Methods · permutations

Problem

Let σ\sigma and τ\tau be the permutations of degree 4 defined by σ1=2\sigma 1 = 2, σ2=3\sigma 2 = 3, σ3=4\sigma 3 = 4, σ4=1\sigma 4 = 1, τ1=3\tau 1 = 3, τ2=1\tau 2 = 1, τ3=2\tau 3 = 2, τ4=4\tau 4 = 4. ((a)) Is σ\sigma odd or even? Is τ\tau odd or even? ((b)) Find στ\sigma\tau and τσ\tau\sigma.

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