Consider the permutation σ in S(10) given by
σ = (2, 5, 3)(1, 5, 3, 8)
(a)
Write σ as a product of disjoint cycles.
(b)
Write σ using matrix notation for permutations.
(c)
Compute the order of σ.
(d)
Compute the sign of σ.
For both (c) and (d), make sure to briefly explain your reasoning.