A right inverse of $A\in\mathbb F^{m\times n}$ is $R\in\mathbb F^{n\times m}$ with $AR=I_m$. It exists exactly when $A$ has full row rank $m$, requiring $n\ge m$. Over $\mathbb R$ or $\mathbb C$, a choice is $R=A^*(AA^*)^{-1}$.
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