The easy way: the invisibility spell also turn invisible the magical emanations that Detect Magic would pick.
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Detect Magic works against invisibility AFTER 3 rounds of concentration.
Example: you are focusing on a specific area and there is a creature with invisibility cast upon it in that area.
In the first round of concentration you detect that there is magic in the area.
In the second you detect that the number of auras (including the illusion aura from the invisibility spell).
In the third round you locate the aura and determine the type of aura.
Note: The invisible creature can just move out of the area being detected.
Note2: Just because you located the aura does not mean there is an invisible creature. See Player-GM interaction below.
Player: I cast detect magic and focus it straight ahead of me.
GM: You detect something magical in the area.
Player: On my second round I get the number of auras.
GM: There is one aura.
Player: On my third round I know the location of the aura.
GM: There is an aura that is 30' away.
Player: I roll my Knowledge Arcana to determine the aura type. (Success)
GM: The type is illusion.
Player: Huh, do I see what the illusion is on?
GM: Nope
Player: Hrm, could be an invisible creature or it could be an illusion of some sort.
GM: Could be, (rolls perception in secret, players fail). The aura is moving, what is your Flat-footed AC? Oh, he hits. Please make a Fortitude Save.
Player: I roll a 15.
GM: Sorry, you are dead. (The assassin was studying him for the last three rounds.) Everyone else, roll initiative.
A DC20 perception check (within 30 feet) or the special ability scent (easily available to many spellcasters) would have told the player just about the same thing and used a lot less time.
Regarding Constant Detect Magic, there is no text in the constant spell-like ability sections that negates the concentration requirement. Even if you ruled that the concentration requirement is not applicable that does not change that it takes 3 rounds to locate magic auras in a cone. So from the moment you designate the area it still takes 3 rounds.
Spell-Like Abilities: After listing the caster level of the creature’s spell-like abilities, this section lists all of the creature’s spell-like abilities, organized by how many times per day it can use the abilities. Constant spell-like abilities function at all times but can be dispelled. A creature can reactivate a constant spell-like ability as a swift action.
A spell-like ability usually has a limit on how often it can be used. A constant spell-like ability or one that can be used at will has no use limit; unless otherwise stated, a creature can only use a constant spell-like ability on itself. Reactivating a constant spell-like ability is a swift action. Using all other spell-like abilities is a standard action unless noted otherwise, and doing so provokes attacks of opportunity. It is possible to make a concentration check to use a spell-like ability defensively and avoid provoking an attack of opportunity, just as when casting a spell. A spell-like ability can be disrupted just as a spell can be. Spell-like abilities cannot be used to counterspell, nor can they be counterspelled.
Summary: While Detect Magic can detect the location of an invisibility spell's illusion aura it takes 3 rounds to do so and that still does not indicate "invisible creature be here". It only indicates "illusion aura be here".
I can tell you in what general area/direction an invisible creature is located, but not the specific square. Once the creature's general location has been pinned down, however, glitterdust can take care of the rest (in a pinch, a bucket of paint should do the trick, also).
Tassel, the first round gets you "is there magic in the area". It is almost worthless information if there are multiple auras.
If your own party is in the area the answer is going to (usually) default to something like: Of course there is magic in the area, your fighter with that shiny +1 sword is in the area. :)
Round two is more useful in that it can tell you the number of auras. If you know the number of auras the "fighter" in your way has then this is the step where you can determine if there are other auras.
Round three is still the same, you know where the auras are and can determine school of aura.
Regarding your question about "kf spells", I am not sure what you mean. But assuming you mean polymorph, they detect the aura (transmutation school) but that does not allow them to see past the polymorph.
Using Detect Magic to chase an invisible creature is pointless. You have to concentrate on each area for 3 rounds for detect magic to locate the aura.
Assuming you are up front (no allied magic getting in the area) you *might* be able to chase him and use "presence of magic" to keep a reasonable idea of his location (he is somewhere in the cone). However, it would limit you to one move action per turn, he can easily outrun you and even if he were slow any new magic would screw it up.
Thank you very much everyone, mostly gauss i didnt thought that way. Ok then i know how it would work on an invisible or on a ilusion spell casted in a place, but if the players, have for example a pcreature using alter self, polymorph or what else, in their front, it would be the same?? They would now that the man/woman, has magic and after 3 rounds of concentration they would know wich auras are on effect and were are the auras??
After 3 rounds they would know there is a transmutation spell on the creature in question. Thats it. It could be alter self it could be bulls strength.
If a non-player creature/humanoid, whatelse is using this kind kf spells, would he/it completly had an aura of the appropiate school, transmutation, i think? Or would not? And what would the pjs see? Just its new form ( the one the creature is getting using the spell) with the aura, or creature's real formwith the aura?
Detect magic doesnt provide and visual feed back, just infromation. "There is a weak transmutation aura 20 ft in front of you". They dont see anything. In fact there is a higher level spell, arcane sight that does that. They dont 'see through spells' or anything like that, even illusions, what they see is unchanged with detect magic. It takes true seeing to do stuff like that.
One thing more, if they are chasing a creature that uses invisibility and then moves, and they saw the creature making itself invisible, would players be able to follow it, or would they need to concentrate to know where the aura is? Time more than enough for the creature to scape?? Or could they follow the magic for enpugh turns to be able to locatr the aura and therefore follow it? Or would it be imposoble to follow it?
Detect magic would provide very limited assistance to chasing an intelligent greature who turns invisible. You have to take a standard action to concentrate, so they could only take a normal move, presumably the fleeing creature would run. It would be out of range of detect magic in a single turn. Not to mention since theres no limit on changing direction, a simple 90degree turn would take you out of the 60ft cone of detect magic within the same turn as you cast invisibilty
DM: The creature casts a spell then turns invisible roll perception checks (the dc is really high to spot an invisible creature) - [the creature then moves its speed (assumed 30ft or more) perpendicular to the party, moving it self out of the range of a 60ft cone cast at its previous location]
Player: I roll spell craft to determine the spell he cast *rolls*
DM: He cast invisibility
Player: Ok I cast detect magic
DM: You detect magic no magic (the creature isnt in the cone)
The player could then aim the cone around seaching for the creature, but if its fleeing it is almost certainly going to get away unless it can somehow be cornered.
Note the very interesting addition to the mix of Magic Aura which can alter the kind of auras perceived by Detect Magic...