Digital Matrix

For the 3rd day in a row, I'm solving a problem from recent Dhaka regionals. This time it is problem F - Digital Matrix. It is a very tricky ad hoc problem. No team could solve it during the real time contest. Fudan University came closest to solving it with their solution giving wrong output on only one type of cases. It took them 13 submissions though to come that close.

The problem states that

You are given two N x N square matrices, A and B. Each of the elements of these matrices is an integer between 1 and K (inclusive). You have to convert matrix A into matrix B in minimum number of operations. In each operation you can choose one element of matrix A and change it to any integer between 1 and K (inclusive). You have to ensure that after any operation the matrix is not converted to a symmetric matrix.