Let A be a particular vector in R22. Determine whether the following are subspaces of R22. (a)

Question:

Let A be a particular vector in R2×2. Determine whether the following are subspaces of R2×2.
(a) S1 = {B ∊ R2×2 | AB = BA}
(b) S2 = {B ∊ R2×2 | AB ≠ BA}
(c) S3 = {B ∊ R2×2 | BA = 0}
Determine whether the following are spanning sets for R2.