Verify that the Galois imaginary is primitive in GF(3, x³ + 2x+1)

Jn is simply an nxn matrix with only ones inside.

Exercise 2.2.3 Let c₁=2i, c₂ = 1+2i, and A = 1-i 2+2i 3 4+i Verify Properties (vi) and (viii) in showing 2x2 is a complex vector space.

3. (12) Let V = R². Define vector addition and scalar multiplication as follows: (u1, uz)O(v1, v2) = (u1V1, U2V2) and c(u1,u2) = (u,C, u2^), c > 0 (a) Does V have an additive identity? If so, what would it be? (b) Does the distributive axiom c(uOv) = cu@cv hold? (Show why or why not). 4