Let M {\displaystyle {}M} be an m × n {\displaystyle {}m\times n} -matrix and φ : K n → K m {\displaystyle {}\varphi \colon K^{n}\rightarrow K^{m}} the corresponding linear mapping. Show that φ {\displaystyle {}\varphi } is surjective if and only if there exists an n × m {\displaystyle {}n\times m} -matrix A {\displaystyle {}A} such that M ∘ A = E m {\displaystyle {}M\circ A=E_{m}} .
