It is a terrible question.

First, you can't invert a binary tree (as in flip upside down). If you did, you'd end up with multiple roots and since all binary trees are rooted, you'd no longer have a binary tree. It'd be a tree, just not a binary tree.

If the questioner meant mirror a binary tree (swap left & right at each node), then it is a no-op. You do not need to modify memory to do it. Left & right are just labels for two pointers. You can just swap the order your variables in whatever struct defines your node and cast it against your existing memory (or change what your accessors return in a derived class or create a reverse iterator or however you want to implement it) and there you go, a "reversed" tree with zero overhead.

Either way, it is a terrible question unless you wanted to see if someone understood the difference between how a data structure is drawn on a whiteboard for humans vs. how it actually works. Maybe they were actually asking that question, but that seems highly unlikely.

And if they actually meant for you to recurse down and swap left and right on everything, it would dramatically lower my opinion of them because it would make me wonder if they knew the difference between how a binary tree is drawn on a whiteboard vs. how it is laid out in memory.