The effect is similar to that of a detect magic spell, but Arcane Sight does not require concentration and discerns aura location and power more quickly.
Arcane Sight says it works as Detect Magic, then lists the exceptions, of which none say it shouldn't work on invisible creatures.
Things you can tell if there is an invisible creature that's within your 60' cone:
- There is something with a magical aura within your sight;
- The exact location of this aura;
- Any other magic aura on this invisible creature.
And assuming you pass a Knowledge(Arcana) check:
- School of this aura as Ilusion;
Are you able to spend the standard action to focus on where the invisible creature is and tell if it is a spell caster and all the other possible information you can glean?
If you do spend a Standard Action to analyze this creature, you do obtain information about its spellcasting abilities, or if the creature can use spell-like abilities.
If you concentrate on a specific creature within 120 feet of you as a standard action, you can determine whether it has any spellcasting or spell-like abilities, whether these are arcane or divine (spell-like abilities register as arcane), and the strength of the most powerful spell or spell-like ability the creature currently has available for use.
However, it says: If you concentrate on a specific creature within 120 feet of you. If the creature is invisible, all you see is her aura, not the creature herself.
For that you would need True Seeing, or Goggles of True Sight:
The subject sees through normal and magical darkness, notices secret doors hidden by magic, sees the exact locations of creatures or objects under blur or displacement effects, sees invisible creatures or objects normally, sees through illusions, and sees the true form of polymorphed, changed, or transmuted things.
It's worth mentioning that True Seeing is a 6th level spell, while Arcane Sight is a 3rd level spell, and Detect Magic is merely a 0th level spell (cantrip/orison/knack).