What is the unstable space of $0$ with respect to this matrix

Question

$$A = \begin{bmatrix} 2 & 0 \\ 0 & 1/2 \\ \end{bmatrix}$$ I was told that the unstable space $W^u(0) = \{ (x,y) \in \mathbb R^2: \lim_{n \to -\infty} A^n \cdot(x,y) = (0,0) \}$ is the $x$-axis, but I think the unstable sapce is $\mathbb R^2$ \ the $y$-axis because for any points in $\mathbb R^2$ \ the $y$-axis, its $x$ coordinate tends to infinity. Is my answer correct?