Finding the subspace of linear transformation

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Is either A or B subspace of $L(R^4,R^5)$ where $L(R^4,R^5)$ denote the set of all linear transformation form $R^4$ to $R^5$

A) $ (T\in L(R^4,R^5)|rank(T)\leq 0)$

B) the set of all $T∈L(R^5,R^4)$ such that there exist bases B and C for $R^5$ and $R^4$, respectively,such that $Mat_{B,C} (T)$ is the zero matrix

My answers

A) it is a subspace as the it only possible when T=0 which is the trivial subspace

B)This is also the trival subspace, so it is a subspace