I have seen this question asked many times here for example: Why is inverse of orthogonal matrix is its transpose?
I understand how the answers on that question proves it.
But I want to understand it from the approach of computing the inverse
If we look at tutorials on computing the inverse.
It says to swap a and d in the diagonal.
for example in this tutorial:
https://www.mathsisfun.com/algebra/matrix-inverse.html
it seems to me that this wouldn't give the transpose because a and d should stay in the same place for the transpose.