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?

**Answer**

Is (A−1)T=(AT)−1 you ask.

Well

AT(A−1)T=(A−1A)T=IT=I(A−1)TAT=(AA−1)T=IT=I

This proves that the inverse of AT is (A−1)T. So the answer to your question is yes.

Here I have used that

ATBT=(BA)T.

And we have used that the inverse of a matrix A is exactly (by definition) the matrix B such that AB=BA=I.

**Attribution***Source : Link , Question Author : Void Star , Answer Author : Thomas*