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

You are given a 0-indexed 2D integer array nums. Initially, your score is 0. Perform the following operations until the matrix becomes empty:

From each row in the matrix, select the largest number and remove it. In the case of a tie, it does not matter which number is chosen.
Identify the highest number amongst all those removed in step 1. Add that number to your score.

Return the final score.
 
Please complete the following python code precisely:
```python
class Solution:
    def matrixSum(self, nums: List[List[int]]) -> int:
```