Compute matrix trace and support updates

Given an n x n integer matrix M, implement a function trace (M) that returns the sum of its main diagonal. Follow-ups: (a) If you receive q point updates (i, j, val) changing M[i][j] to val, design a data structure to return the current trace after each update in O(

1. time; (b) Extend the function to also compute the anti-diagonal sum efficiently; (c) Discuss time and space complexities and edge cases (non-square input, large n).