Hi everyone, I am having difficulty solving the following question: Prove that the set V=R^2 with addition defined by (x,y)+(x'+y')=(x+x'+1, y+y') and scaler multiplication by k(x,y)=(kx+k-1, ky) is a vector space, find-(x+y) and the zero vector in this vector space. the following was my attempt: -(x,y)=(-1)(x,y)=((-1)x+(-1)-1), (-1)y)=(-x-1, -y) (Is this correct?) Also, how to find the zero vector in this vector space? I do not know where to start for this one. Any thoughts? Thanks in advance!