Depends on how you look at it, I guess. A binary tree has a couple of properties. Usually there is some ordering on the type. Something like: the element on the left is smaller than the element on the right. (e_L < e_R). Invert would be than turning the ordering into e_R > e_L. I guess this is the left and right branches exchange answer.
If you see a binary tree T e as some kind of function, it can test whether an element exists, a typical set operation. So f : e -> {0,1}, where (e,1) means the element is in the binary tree. (e,0) means it is not in the binary tree. All those (e,0) creates some sort of complement tree, which might also be seen as inverting it.
What would be really weird is seeing it as a directed acyclic graph and invert the direction of every edge.
If you see a binary tree T e as some kind of function, it can test whether an element exists, a typical set operation. So f : e -> {0,1}, where (e,1) means the element is in the binary tree. (e,0) means it is not in the binary tree. All those (e,0) creates some sort of complement tree, which might also be seen as inverting it.
What would be really weird is seeing it as a directed acyclic graph and invert the direction of every edge.