Suppose one has an $n \times n$ matrix whose entries are filled with the numbers $1,2,\ldots,n^2$, but not in that order.
Q1: What is the largest number of row or column swaps ever needed to end up with the entries sorted, e.g., for $n=3$, to reach this matrix: $\left( \begin{array}{ccc} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{array} \right) $ A row swap interchanges two rows; a column swap interchanges two columns. So I am asking for the most disordered matrix with respect to swaps.
Q2: If the $n^2$ numbers are randomly placed, what is the expected minimum number of row and column swaps needed to sort the matrix?
I have no doubt these questions have been explored and answered, but I must not be searching under the right terminology. Thanks for your help!