In general the construction with the inversion does not work with the first person singular (je = I). In these cases the question is formed with
est-ce que.
Examples
J' ai acheté un livre. =>
Est-ce que j' ai acheté un livre?
NOT: Ai-je acheté un livre?
I have bought a book.=>
Have I bought a book?
(To be very precise - in some cases of very often used verbs, the inversion can be used, but it is not common to do so.)
