Abstract Algebra Permutation Groups Identity is Even

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Just able to understand from book but from this video it's easy

ashishsaxena
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Im confused at the second slide. How did you know (b c a) = (b c)(b a)? Or (c b a) = (c b)(c a)?

zhengyangfei
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Hello, I have a trouble understanding the part when the proof uses induction hypothesis that k-2 is even. Wouldn’t it assume the conclusion? Obviously, when k-2 is even, then k is really even. Why is the statement k-2 is even the induction hypothesis? thank you!

jpbstamaria