I can’t seem to find the answer to this using Google.
Is the transpose of the inverse of a square matrix the same as the inverse of the transpose of that same matrix?
Is (A−1)T=(AT)−1 you ask.
This proves that the inverse of AT is (A−1)T. So the answer to your question is yes.
Here I have used that
And we have used that the inverse of a matrix A is exactly (by definition) the matrix B such that AB=BA=I.