Can moment of inertia be negative?

Actually, the answer can be yes.

When we are talking about simple ##I_(x x)## or ##I_(y y)## values, then yes these will always be positive. However, when talking about moment products like ##I_(x y)##, these will not necessarily be positive, mainly when holes have been cut in these cross sections.

When the holes are cut in, those moments then become negative, and due to the parallel axis theorem sometimes these negative values actually become larger than the initial value, and the moment then becomes negative.

Yes I know this question was posted a long time ago, but this was the first hit on Google and wanted to post in case the other answers confused anybody.