Assignment:
Q1. If alpha is an r-cycle, show that alpha^r = (1). [There's a hint that If alpha = (i sub 0 ... i sub r-1), show that alpha ^k(i sub 0) = i sub k.]
Q2. Show that an r-cycle is an even permutation if and only if r is odd.
Q3. If alpha is an r-cycle and 1
Provide complete and step by step solution for the question and show calculations and use formulas.