let check option by option,
option A:-
$P^{-1} = \frac{1}{4}(3P-P^2) $
$4.P^{-1} = (3P-P^2) $
multiply by P
$4I = (3P^2-P^3) $
this is the characteristic eqn, so substitute $\lambda$
$\lambda=2$, then 4 = 12-8 ===> satisfies
$\lambda=-1$, then 4 = 3-(-1) ===> satisfies
so A is correct option !