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Let $R$ be an euclidean domain, and $A$ a $m\times n$ matrix. I want to prove two things:

1) The torsion submodules of $\mathrm{Coker}\;A$ and $\mathrm{Coker}\;A^T$ are isomorphic.

2) $\mathrm{Coker}\;A$ and $\mathrm{Coker}\;A^T$ are isomorphic is and only if $n=m$.

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