How can I determine the automorphism?

Question

How can I determine $$Aut(\Bbb Z_{2} \oplus \Bbb Z_{2})?$$ Is $$Aut(\Bbb Z_{2} \oplus \Bbb Z_{2})\equiv S{3}?$$ Generators goes to generator under automorphism. There are 3 elements in$(\Bbb Z_{2} \oplus \Bbb Z_{2})$ of order 2. But I can get any conclusions from this concept.

Answer 1

Hint: $\mathbb Z_2 \oplus \mathbb Z_2$ is a $\mathbb Z_2$ vector space with basis $(1,0),(0,1)$.