Find the characteristic polynomial of the matrix A=(2005)A = \begin{pmatrix} 2 & 0 \\ 0 & 5 \end{pmatrix}A=(2005).
(λ−2)(λ−5)=λ2−7λ+10(\lambda - 2)(\lambda - 5) = \lambda^2 - 7\lambda + 10(λ−2)(λ−5)=λ2−7λ+10
(λ+2)(λ+5)=λ2+7λ+10(\lambda + 2)(\lambda + 5) = \lambda^2 + 7\lambda + 10(λ+2)(λ+5)=λ2+7λ+10
λ2−10=0\lambda^2 - 10 = 0λ2−10=0
(2λ−5)=0(2\lambda - 5) = 0(2λ−5)=0