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 $n=m$.