Necessarily versus possibly

1. A.There exists a vector $v \in \mathbb{R}^{10}$ such that Av ≠ 0 and $A^{2}v = 0$
2. B.There exists a vector $v \in \mathbb{R}^{10}$ such that $A^{2}v \ne 0$✓ Correct
3. C.A must have a non-zero eigenvalue
4. D.$A^{7} = 0$

The trap it tests

p-values, size, power and error types say specific things. This was not one of them.