This card’s ability does not override effects which prevent a permanent from untapping.

Permanents with multiple types untap if any of their types is chosen. For example, an artifact creature untaps if either artifact or creature is chosen.

If another effect limits the number of permanents that untap, that number combines with Storage Matrix’s effect. For example, Imi Statue says “players can’t untap more than one artifact during their untap steps.” If both Imi Statue and an untapped Storage Matrix are on the battlefield, and you choose “artifact,” only one artifact untaps.