Write the integer which is its own additive inverse.
$$\bullet$$ Additive inverse of a positive integer is a negative integer.
$$\bullet$$ Additive inverse of a negative integer is a positive integer.
$$0$$ is an integer, but it is neither positive nor negative.
Additive inverse of $$0$$ is also $$0$$.
$$\therefore$$ $$\textbf{Zero is the integer which is its own additive inverse}$$.