Let $A \in \mathbb C^{m \times n}$ with $m \geq n$, of rank $n$. Prove there is $B \in \mathbb C^{n \times m}$: $BA=Id_n$.
I have no idea how to solve the problem, I would appreciate suggestions.
2026-03-27 14:57:56.1774623476
Matrices and rank exercise
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HINT: The reduced echelon form of $A$ is $\begin{bmatrix} I \\\hline O \end{bmatrix}$. Now obtain the reduced echelon form by multiplying $A$ by a product of elementary matrices.