Does a simple casting of Detect Magic reveal the presence of magical invisibility?
Yes. And the quotation to back this up comes from the PRD glossary on invisibility where it says almost at the bottom:
Invisibility does not thwart divination spells.
If we look up Detect Magic it says plainly that it is of the divination school. Thus it can be used to detect the aura from magical invisibility.
Indirectly confirming this is the fact that the new Mythic Adventures invisibility spell specifically says:
The invisible target can't be detected with detect magic or other spells that detect magic auras. The invisibility can't be penetrated, revealed, or dispelled by spells of 2nd level or lower (such as see invisibility or glitterdust), though true seeing and dust of appearance can reveal the invisible target's presence.
It's therefore pretty clear that per the RAW, Detect Magic will indeed reveal the presence of (non-mythic) magical invisibility.
1\$\begingroup\$ Since this answer's at the top, I just want to note @Zachiel's comment in the other answer that the creature's square is pinpointed, but the creature still has total concealment relative to the detect magic beneficiary. \$\endgroup\$ Oct 4, 2016 at 22:18
Invisibility does not conceal any aura, it just fouls sight. You also need a way to hide auras if you want your character/item to be undetectable.
4\$\begingroup\$ Worth noting that an invisible creature still has Total Concealment under detect magic. \$\endgroup\$– KRyanNov 23, 2013 at 1:35
\$\begingroup\$ Wonderful. Is there a source/reference/link to a definitive answer or perhaps something in the book I missed that makes this clear? \$\endgroup\$ Nov 23, 2013 at 2:10
3\$\begingroup\$ I'm working by logic, by just looking at the spell's description on the SRD. Invisibility never talks about concealing any aura. Invisibility is a spell, so it has an aura. Detect Magic lets you see auras, which are not made invisible. \$\endgroup\$– ZachielNov 23, 2013 at 13:43
Presence, yes. But the most basic use of the spell only says that something is there, not where it is, so it wouldn't spoil the invisibility effect.
To actually get an idea of where the invisible person is, you'd have to concentrate for a couple of rounds. Two rounds is enough if the invisibility spell is the strongest in the area, but that's easy to camouflage by putting a stronger aura somewhere else. You'd have to concentrate for three rounds to be guaranteed to nail down an invisible person's location.
2\$\begingroup\$ Not so good in the heat of combat but maybe good for finding an object like a gem or treasure chest that has been 'cloaked'. \$\endgroup\$ Nov 23, 2013 at 10:18