Max within groups

I know there's a really easy way to do this but I just can't track  
it down. I experimented with various apply functions but couldn't  
get it quite right.

I have a matrix like this:

1, 16
1, 23
1, 21
1, 6
1, 25
2, 4
2, 17
2, 45
2, 11
2, 20

and I'd like to find the max value in Column 2 (or the index to the  
max value) grouped by the first column. So the max for Group 1, the  
max for Group 2 etc.

Any help would be appreciated.

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