Which of the following are NOT required for a vector space? Check all that apply.
a. Commutativity of vector multiplication: ( u v )
b. Associativity of vector addition: ( u + v = v + u )
c. Existence of additive identity: There exists ( 0 ) such that ( v + 0 = v )
d. Existence of additive inverses: For every ( v ), there exists ( -v ) such that ( v + (-v) = 0 )