Please solve the programming task below using a self-contained code snippet in a markdown code block.

You are given an n x n integer matrix. You can do the following operation any number of times:

Choose any two adjacent elements of matrix and multiply each of them by -1.

Two elements are considered adjacent if and only if they share a border.
Your goal is to maximize the summation of the matrix's elements. Return the maximum sum of the matrix's elements using the operation mentioned above.
 
Please complete the following python code precisely:
```python
class Solution:
    def maxMatrixSum(self, matrix: List[List[int]]) -> int:
```