It seems a simple enough question,
Can you? Of course; you just did. Your characters, I might point out, are not inaminate. They are alive. They have thought, opinion, and agency. They may be made of silicon, but they are not "inanimate."
Someone on this board recommended a story told from the viewpoint of a sentient pregnancy test. Anything is possible with the right execution.
Russell Hoban's underappreciated novel Kleinzeit features a large cast of unusual characters, including a fair number of inanimate objects, such as "The Paper" and "The Hospital." However, they are all anthropomorphized --they speak and act like human beings. Similarly, your own example stretches the definition of inanimate --a sentient artificial intelligence may not technically be "animate," but it certainly isn't even an unusual character for a science-fiction book.
A work centering entirely around a cast of non-animate, non-sentient objects would be a challenge to pull off, because they don't have any agency or capacity for change. However, never say never: https://www.youtube.com/watch?v=ZdIJOE9jNcM (Wikipedia: Lamp)