Let F be a field of 5 elements Fill out the multiplication a

Let F be a field of 5 elements. Fill out the multiplication and addition tables for F.

Solution

multiplication tables:

addition tables:

5-5=0 ,0 write on right hand side and carry 1.so 10 with base 5.

similarly,6-5=1,write on right hand side and carry 1.so 11 with base 5.

x5	0	1	2	3	4
0	0	0	0	0	0
1	0	1	2	3	4
2	0	2	4	11	13
3	0	3	11	14	22
4	0	4	13	22	31