Groups and FieldsHardPermutation Groups SharePermutation Groups · Hard problemLet α=(1 2 3)(4 5)∈S6\alpha=(1\,2\,3)(4\,5) \in S_6α=(123)(45)∈S6 and β=(1 4)(2 3 6)∈S6\beta=(1\,4)(2\,3\,6) \in S_6β=(14)(236)∈S6. Without computing the product αβ\alpha\betaαβ in full, is αβ\alpha\betaαβ even or odd?AevenBoddCodd, because both α\alphaα and β\betaβ are individually oddDcannot be determined without multiplying α\alphaα and β\betaβ out in fullCheck Show answer Walk through it step by step Practice more like this Review this concept