I want to show, that $GL_n(\mathbb{Z}/b\mathbb{Z})$ operates transitively on $X = \{ (v_1, \ldots, v_n) \in (\mathbb{Z}/b\mathbb{Z})^n \ | \ v_1\mathbb{Z}/b\mathbb{Z} + \ldots + v_n\mathbb{Z}/b\mathbb{Z} = \mathbb{Z}/b\mathbb{Z}\} $
($b$ is an integer.)

IOW

1. $A \in GL_n(\mathbb{Z}/b\mathbb{Z}), x \in X \Rightarrow Ax \in X$
2. For all $x,y \in X$ exists $A \in GL_n(\mathbb{Z}/b\mathbb{Z})$ such that $x = Ay$.

I have no idea, where to start.

Thanks
-elfinit