2. $AD\rightarrow 3(\times n \times n) \times 2 \rightarrow 3\times 2 \rightarrow R^{3\times 2},AD=I_3?$, Are you sure ?
$if\ D\in R^{n\times 3},D=[\vec{v}_1,\vec{v}_2,\vec{v}_3], find\ AD=I_3,$
We could do $AD=A[\vec{v}_1,\vec{v}_2,\vec{v}_3]=[A\vec{v}_1,A\vec{v}_2,A\vec{v}_3]=[\vec{e}_1\ \ \vec{e}_2\ \ \vec{e}_3]$
To resolute $A\vec{v}_i=\vec{e}_i$ is easy.