Let e € Sn be the identity. Assume that e = B1B2. Br, where B₁, B2,... Br are 2-cycles. Choose the correct option from below and explain why. (a) r is always odd. (b) r is always even. (c) r can be odd or even, it depends on the specific decomposition that we use.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
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Let e € Sn be the identity. Assume that e = B1B2. Br, where B₁, B2,... Br are 2-cycles. Choose the
correct option from below and explain why.
(a) r is always odd.
(b) r is always even.
(c) r can be odd or even, it depends on the specific decomposition that we use.
Transcribed Image Text:Let e € Sn be the identity. Assume that e = B1B2. Br, where B₁, B2,... Br are 2-cycles. Choose the correct option from below and explain why. (a) r is always odd. (b) r is always even. (c) r can be odd or even, it depends on the specific decomposition that we use.
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