In the space of polynomials of degree 2 or less, given the derivative linear transformation D and $T:=1+D+D^2$, $S:=1-D$, show that $S=T^{-1}$

Question

Let $ P_2[X] $ be the space of polynomials of degree equal or less than 2 over the field R. Let: $$ D: P_2[X] \rightarrow P_2[X] $$ Be the derivative linear transformation, defined as follows: $$ (D(P))(X) = P'(X) $$ Also: $$ T := 1 + D + D^2 $$

$$ S := 1 - D $$

Show that $ S = T^{-1} $