What is the characteristic polynomial of the permutation matrix P=(010001100)P = \begin{pmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \end{pmatrix}P=001100010?
p(λ)=λ3−1p(\lambda) = \lambda^3 - 1p(λ)=λ3−1
p(λ)=λ3+1p(\lambda) = \lambda^3 + 1p(λ)=λ3+1
p(λ)=1−λ3p(\lambda) = 1 - \lambda^3p(λ)=1−λ3
p(λ)=(λ−1)3p(\lambda) = (\lambda - 1)^3p(λ)=(λ−1)3