Basic questions on Picard group (references)

Question

I want a reference/explanation for things as follows. For nice enough commutative ring $A$, we have $Pic(A[[x]]) \cong Pic(A)$. Also, I want to know about comparing $Pic(A((x)))$ and $Pic(A)$, for example to know things like $Pic(k[[x_1]]((x_2))) = 1$.

Thanks!