How to determine whether inversion takes place? Predict in which of the following reaction inversion of configuration takes place:
  


In my view, C) involves $\mathrm{S_{N} i}$ and therefore doesn't involve inversion of configuration. In D) the syn addition of $\ce{H2}$ across the double bond takes place and doesn't change the configuration. However I am not sure about A) and B).  Any ideas?
A) is $\mathrm{S_N2}$ due to the secondary $\ce{C}$ and the sufficiently good nucleophile $\ce{I-}$. So inversion takes place.
B) is $\mathrm{S_N1}$ due to the tertiary $\ce{C}$. The solvent is also more polar than in A). So the stereochemical information would be lost.