Rank is field independent

1. A.{$v\in {\mathbb{Q}}^5$ | Bv = 0} is a three-dimensional vector space over $\mathbb{Q}$.✓
2. B.The linear transformation $T:{\mathbb{Q}}^3\to {\mathbb{Q}}^5$ given by T(v) = Bᵗv is injective.
3. C.The column span of B is two-dimensional.✓
4. D.The linear transformation $T:{\mathbb{Q}}^3\to {\mathbb{Q}}^3$ given by T(v) = BBᵗv is injective.

The trap it tests

Base field or ring

The answer changes with the field or ring you are working over.