Nilpotent index from nullity

1. A.The rank of T is equal to 2.
2. B.Suppose that for every vector $v\in {\mathbb{R}}^5$ there exists n such that $T^{n}v=0$. Then $T^2$ must be zero.
3. C.Suppose that for every vector $v\in {\mathbb{R}}^5$ there exists n such that $T^{n}v=0$. Then $T^3$ must be zero.
4. D.(−2, −8, 3, 2, 0) is contained in the null space of T.

The trap it tests

Invariants don't determine

Two objects sharing an invariant were treated as the same object.