Randomly remove some numeric data from a matrix in R?

I have a large data matrix with many numeric values (counts) in it. I would like to remove 10% of all counts. So, for example, a matrix which looks like this:

30 10
 0 20

The sum of all counts here is 60. 10% of 60 is 6. So I want to randomly remove 6. A correct output could be:

29 6
 0 19

(As you can see it removed 1 from 30, 4 from 10 and 1 from 20). There cannot be negative values.

How could I program this in R?