I have a repository with branches master and A and lots of merge activity between the two. How can I find the commit in my repository when branch A was created based on mast
You may be looking for git merge-base:
git merge-base finds best common ancestor(s) between two commits to use in a three-way merge. One common ancestor is better than another common ancestor if the latter is an ancestor of the former. A common ancestor that does not have any better common ancestor is a best common ancestor, i.e. a merge base. Note that there can be more than one merge base for a pair of commits.