In the sentence, "I'm cleaning my room," Cleaning is the verb, my is the possessive adjective. Which is the subject and why?

"I" because it is "I" that is cleaning.

In this question, we have:

"I'm cleaning my room"

I'll now substitute in the parts of speech for each word:

"Subject, Verb, Posessive Adjective, Object".

I is the subject because it is "I" that is cleaning. What is "I" cleaning? The room - which makes "the room" the object of the cleaning.