Let $\mathcal { P } _ { n } = \{ f ( x ) \in \mathbb { R } [ x ] \mid \operatorname { deg } f ( x ) \leq n \}$, considered as an ($n + 1$)-dimensional real vector space. Let $T$ be the linear operator $f \mapsto f + \frac { \mathrm { d } f } { \mathrm {~d} x }$ on $\mathcal { P } _ { n }$. Pick the correct statement(s) from below.\\
(A) $T$ is invertible.\\
(B) $T$ is diagonalizable.\\
(C) $T$ is nilpotent.\\
(D) $( T - I ) ^ { 2 } = ( T - I )$ where $I$ is the identity map.