What is an antiunitary operator? What is an antiunitary operator? In field theory one can define a time reversal operator $T$ such that $T^{-1} \phi (x) T = \phi (\mathcal T x)$. It is then proved that $T$ must be antiunitary: $T^{-1} i  T = -i$.
How is this equation to be understood? If $i$ is just the unit complex number, why don't we have $T^{-1} i  T = i T^{-1} T$ which is just the identity times $i$?
 A: As Qmechanic noted, $T$ is antilinear (this is part of the definition of being antiunitary).  Of course, $T^{-1}$ must be antilinear as well because $T$ is.  Thus, for any vector in this Hilbert space $v$, $T^{-1}(iv)=-iT^{-1}(v)$.  The $i$ pops out as a $-i$.  Applying this to your equation, we easily have that
$$
T^{-1}iT=-iT^{-1}T=-i.
$$
A: If I correctly understood your misunderstanding, the answer is: operator is not always a matrix. Technically, action of time inversion operator contains complex conjugation. 
E.g., in spin up/spin down basis it is written as $-i\sigma_y\mathcal{K}$, where $\mathcal{K}$ is complex conjugation. 
A: I think that just wrong (the wikipedia thing)


*

*$i \in \mathbb C$ so how can an operator act on a scalar?

*Even if it was right, one knows that $T = T^\dagger = T^{-1} = -T^*$. So take what you read


$$TiT^{-1} = -i$$ 
and now treat $i$ as an scalar (what is! not a pseudo-!) and it turns out 
$$Ti(-T)^* = -T^2 i = -i \Rightarrow T^2 = 1$$
that is what we know about $T$ so it should be wrong that thingy of Wikipedia... ;).
The only real explanation could be a phase, not that $i$ changes it sign when you tossed it with $T$.
