# Transpose of inverse vs inverse of transpose

Is the transpose of the inverse of a square matrix the same as the inverse of the transpose of that same matrix?

Is $(A^{-1})^T = (A^T)^{-1}$ you ask.
This proves that the inverse of $A^T$ is $(A^{-1})^T$. So the answer to your question is yes.
And we have used that the inverse of a matrix $A$ is exactly (by definition) the matrix $B$ such that $AB = BA = I$.