  Drinfeld-modules and $A$-motives are the function field analogous of elliptic
curves and abelian varieties. For the latter one can construct the $l$-adic
Galois representation and can ask if its image is open. For Drinfeld-modules
this question was answered by Pink and his coauthors. We clarify the rank one
case for $A$-motives and show that the image of Galois is open if and only if
the virtual dimension is prime to the characteristic of the ground field.
