Question

The order of 3 in the group (Z12,+12)is
a.2
b.4
c.6
d.8​

Answer 1

Answer:

6 is the answer i think, i just think hehe

Answer 2

Answer:

The order of 3 in the group  $(Z_{12} ,+_{12})$  is 4.

Step-by-step explanation:

Let $G$ be a group. The order of an element $a$ in $G$ is the smallest positive integer $n$ such that

$a^n=e$

where $e$ is the identity in  $G$.

Given the group, $(Z_{12} ,+_{12})$ with the operation addition modulo 12.

We have to find the order of element 3. we have

$(3+3+3+3)_{+_{12}} = 12_{+_{12}} =0$

When we add 3 four times we get the identity element 0. Thus the order of 3 is 4. Option b is the right answer.