Let \( A=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right] \)...
Let \( A=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right] \) and \( f(\lambda)=\operatorname{det}(A-\lambda I) \), then
(a) \( f(\lambda)=\lambda^{2}-(a+d) \lambda+a d-b c \)
(b) \( f(A)=0 \)
(c) \( A^{2}=O \) implies \( A^{r}=0 \forall r \geq 2 \)
(d) none of these
\( \mathrm{P} \)
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