Given the operation in RR^2: (x_1,y_1)+(x_2,y_2)=(x_1x_2,y_1y_2) I would like to find whether this is a vector space in RR. Looking at the Additive Zero Axiom, we get: (x_1,y_1)+0=(x_1(0),y_1(0))=0 To satisfy the Additive Zero Axiom, (x_1,y_1)+0=(x_1,y_1) must be true. For this to be true, 0 would have to be (1,1) Is this possible, or would we be able to say this is not a vector space?

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