True/False Question :
The set of nilpotent matrices in $M_{3}\left ( \mathbb{R} \right )$ spans $M_{3}\left ( \mathbb{R} \right )$ considered as an $\mathbb{R}$-vector space (a matrix $A$ is said to be nilpotent if there exists $n \in \mathbb{N}$ such that $A^{n}=0$).