Considere as matrizes $$A=\left(\begin{array}{lll}2& 0& 1\\ 0& 2& 0\\ 1& 0& 2\end{array}\right)$$$$B=\left(\begin{array}{lll}-1& 0& 1\\ 0& -2& 0\\ 1& 0& -1\end{array}\right)$$Sejam ${\lambda }_0$, ${\lambda }_1$ e ${\lambda }_3$ as raízes da equação $\text{det}(A-\lambda I_3)=0$ com ${\lambda }_0\le {\lambda }_1\le {\lambda }_2$.

Considere as afirmações:

• I- $B=A-{\lambda }_0{I}_3$

• II- $B=(A-{\lambda }_1{I}_3)A$

• III- $B=A(A-{\lambda }_2{I}_3)$

Então: