Inverting a binary tree is easy; express the tree as a matrix (laplacian), invert the matrix, then convert that back to a tree. What the canonical question is asking is not inversion.

Since too many people were memorizing inversion, I switched to asking how to evert a binary tree. This leads naturally into a discussion of the 1:1 relationship between complex numbers and cohomology sets, I figure if somebody can get that right, they can be a junior programmer on the team.

"Flip" or "mirror" is probably a better term. It seems the goal is to swap left and right: https://leetcode.com/problems/invert-binary-tree/