List of list, converting all strings to int, Python 3

I am trying to convert all elements of the small lists in the big list to integers, so it should look like this:

current list:
list = [['1','2','3'],['8','6','8'],['2','9','3'],['2','5','7'],['5','4','1'],['0','8','7']]


for e in list:
    for i in e:
        i = int(i)

new list:
list = [[1,2,3],[8,6,8],[2,9,3],[2,5,7],[5,4,1],[0,8,7]]

Could anyone tell me why doesn't this work and show me a method that does work? Thanks!