i have a sheet with 2 rows: location and activity.

What you describe is 2 columns!

schematic exemple
location activity
1 A
1 B
2 A
3 A
3 B
3 C
4 B
4 C


X A B C
A 0 2 1
B 2 0 2
C 1 2 0


From the example of data and output above i'm not sure this makes
sense. Why would you have ABC across the top AND down the left side?
From the data above would your output not be as follows:

X A B C
1 1 1 0
2 1 0 0
3 1 1 1
4 0 1 1

If this is what you want then you should look into doing a pivot table.
and place "COUNT of Activity" in the 'Data' section, place "Activity"
in the 'Column' Section and place "Location" in the 'Row' section.

HTH