How to mutate a variable within a loop and store all of the mutations in a list?

Question

I have this grid

grid =  [[3, 5, 4, 9, 8, 7, 6, 1, 2],
         [7, 8, 2, 6, 1, 4, 5, 9, 3],
         [9, 1, 6, 2, 5, 3, 4, 7, 8],
         [4, 7, 9, 5, 2, 6,