Long solution matrix part 2

Let A be a $2 \times 2$ matrix. Suppose that for every two-dimensional vector v, there exists a two-dimensional vector w such that $\mathbf{A} \mathbf{w} = \mathbf{v}$
Show that we can find a matrix B such that $\mathbf{A} \mathbf{B} = \mathbf{I}$.