Chapter 4.2, Problem 22P

On ${ℝ}^2$, define the operations of addition and scalar multiplication by a real number as follows:

$\left(x_1,y_1\right)\oplus \left(x_2,y_2\right)=\left(x_1-x_2,y_1-y_2\right)$,

$k\odot \left(x_1,y_1\right)=\left(-k{x}_1,-k{y}_1\right)$.

Which of the axioms for a vector space are satisfied by ${ℝ}^2$ with these algebraic operations? Is this a vector space structure?