"A teacher inspects the students"
Translation:Mwalimu hukagua wanafunzi
I think that is the habitual hu-, not the second person singular negative. You'll learn a bit more about it later in the tree (the verb here is kukagaua. The habitual hu- takes the place of the tense marker, and does not require a subject prefix, hence no a-. It does, however, require a noun or pronoun, which in this sentence is of course mwalimu.)