If I'm carrying a person and use Gaseous Form or Invisibility, is the person I'm carrying also transformed or made invisible?
If no, what if the person is inside a big bag?
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Both spells affect 1 creature and all its "gear". The word "gear" is used inconsistently throughout the rules: sometimes it includes armour and sometimes not, sometimes it includes clothes and sometimes not, sometimes it includes weapons and sometimes not, etc. What it never includes is another creature.
The person inside the bag (if they are alive) is a creature, when you go gaseous the bag joins you and they fall to the floor. If you go invisible than they appear to be floating in the invisible bag.
If they are dead, then there is an argument that they are "gear": DM's call.
If they are in an extra-dimensional space (e.g. Bag of Holding) then they stay in that space.