Does $\left\{0, 1, 2\right\}$ along with the operation of addition $\text{mod } 6$ form a group?
I have many practice questions like this, and I know I have to check closure, associativity, identity, and inverse to see if this forms a group.
I'm not completely clear on how to do this in the given context. Am I supposed to see if $0,1,2$ integers can be closed under addition in $\text{mod } 6$, are associative, have additive identity and inverses?
If so, how would I go about that for this? Is there any methods that would help a beginner understand this problem better?
What you are basically asking if the set $\{\overline{0}, \overline{1}, \overline{2}\}$ is a subgroup of $\mathbb{Z}/6\mathbb{Z}$, the integers mod $6$. Well, the set is not closed since $\overline{2} + \overline{2} = \overline{4}$ is not an element of it.