Let V = {0,1,2} with addition defined by mod 3 and scalar multiplication given by ku=u^{k}mod 3 for all K is an element of real numbers, u is an element of V. Is the set V a vector space?

am I supposed to set u= <u_{1},u_{2},u_{3}> and then go through all the axions to determine whether if it's a vector space?