Write out the addition and multiplication tables for Z6 (where by addition and multiplication we mean +6 and .6).
Step 1</p>
In this problem we have to write the addition and multiplication table for .where, by addition means and by multiplication means .
Arithmetic operations can be defined on as, the set of nonnegative integers less than m,
that is, the set {0, 1,...,m − 1}.
In mathematical form, we define addition of these integers, denoted by by
a b = (a + b) mod m,
where the addition on the righthand side of this equation is the ordinary addition of integers.
and
we define multiplication of these integers, denoted by by
a b = (a · b) mod m,
where the multiplication on the righthand side of this equation is the ordinary multiplication of
integers. The operations and are called addition and multiplication modulo m.
Step 2 </p>
The addition table for is
0 
1 
2 
3 
4 
5 

0 
0 
1 
2 
3 
4 
5 
1 
1 
2 
3 
4 
5 
0 
2 
2 
3 
4 
5 
0 
1 
3 
3 
4 
5 
0 
1 
2 
4 
4 
5 
0 
1 
2 
3 
5 
5 
0 
1 
2 
3 
4 