Identification of dual space

Identification of dual space References Let $Q$ be a finite quiver and let $M$ denote the $k$-vector space generated by all arrows. Let $Q^{\\ast}$ denote the opposite quiver of $Q$, i.e reverse all arrows. Now let $M^{\\ast}$ denote the $k$-vector space generated by all arrows of $Q^{\\ast}$. Why can we identify $M^{\\ast}$ with $Hom_{k}(M,k)$?