/sci/ - Science & Math

Pic related is from Axler's LADW. Is it correct?
My reasoning is that:
> (V -> W) (W -> V) = (V -> V)
> (W -> V) (V -> W) = (W -> W)
So [math]TT^{-1} = I_V[/math] and [math]T^{-1}T = I_W[/math], which is the opposite of what he says.