Laplace expansion needs to exchange mn times, so it is mn. The specific steps are as follows:

1. In the mathematical Laplace expansion, let A and B be M and N orders respectively, and write them in the form of column vectors.

2. The first column of A is exchanged with the previous column in turn, so it takes n times to move to the first column of the whole determinant.

3. Similarly, the second column of the first A has to be moved to the second column of the whole determinant n times, and A has m column vectors, so it needs to be exchanged mn times in total.