Is this question completely defined I saw this question on a page:
If $a$ is additive identity then:
a)$a+a=2a$
(b)$a+a=1$ 
(c)$a+a=a$ 
(d)$a+a=0$
I think the question is undefined,Here the intended answer is c) but I think the question is undefined since the set is not mentioned to which $a$ is additive identity 
Update: I guess a), c) and d) can be the correct answers at the same time or is there an example of a group which only satisfies c)?

In an additive group $(G, +)$ you have a unique (additive) identity $e$. This elements satisfies that $e + g = g$ for all $g \in G$. In particular you have $e + e = e$.
Example: Think about the additive group $\mathbb{Z}$. Here $0$ is the identity because you indeed have $0 + n = n$ for all $n\in \mathbb{Z}$. In particular you have $0+0 = 0$.
So it is pretty obvious that (c) is the right answer since this is the defining property. However, I agree that it might be confusing. 
One could argue that (d) is the right answer because $0$ usually is the "symbol" we use for the (additive) identity, and so you would have $a = 0$ and so (d) would be right. 
(b) definitely isn't the right answer because $1$ usually denotes the multiplicative identity. 
(a) could be considered right since we usually take $2a$ to mean $a+a$ by definition.
