Exercise 2.7.13

Answers

A cyclic

P = [\begin{matrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \end{matrix}]

or its transpose will have

P^{3} = I : (1, 2, 3) \to (2, 3, 1) \to (3, 1, 2) \to (1, 2, 3) .

The permutation

\hat{P} = [\begin{matrix} 1 & 0 \\ 0 & P \end{matrix}]

for the same $P$ has ${\hat{P}}^{4} = \hat{P} \neq I$ .

mathchakra

2022-01-16 12:20