Let $T$ be the linear transformation from the real vector space $\mathbb{R}[x]$ to itself, given by $T(f)=f^{\prime}$, where $f^{\prime}$ is the derivative of $f$. Consider the following statements about $T$ :
- $T$ is nilpotent.
- The only eigenvalue of $T$ is 0.
Which of the following sentences is true?
- Both (I) and (II) are true.
- (I) is true but (II) is false.
- (I) is false but (II) is true.
- Both (I) and (II) are false.
