So I'm currently studying for an exam of linear algebra and there is this exercise that I cannot seem to find even how to start with. The question is the following:
"Let $L: \mathbb{R}^2 \to \mathbb{R}^3 $ be a linear map with a matrix:
A = $ \begin{bmatrix} 2 & 3 \\ 4 & 6 \\ 6 & 9 \end{bmatrix} $
This matrix is defined with respects to the standard basis for both $\mathbb{R}^2$ and $\mathbb{R}^3$ (so $A = L^{\mathbb{R}^3}_{\mathbb{R}^2}$). Find a basis $\alpha$ in $\mathbb{R}^2$ and $\beta$ in $\mathbb{R}^3$ such that $L^{\mathbb{R}^3}_{\mathbb{R}^2}$ is a matrix with the specific shape:
$ \begin{bmatrix} \mathbb{I}_r & 0 \\ 0 & 0 \\ \end{bmatrix} $
(Here $r$ is the rank of the matrix)"
How should I solve this problem? I'm literally stuck since I don't even know how I would start.