This problem seems like a trick question, I am not sure how to approach it.

Is the following a subspace? If so, find the bases and dimension.

P ∈ R[x] ; P^2 = 0

I know that it is a subspace if:

The zero vector is included in the set

Closed under addition

Closed under scalar multiplication

From first glance it seems like a subspace but how do I prove this and would it have a 0 basis?