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?