Is $O(2)$ unimodular? (i.e. it left Haar measure is also right invariant.)

Question

Is $O(2)$ unimodular? (i.e. it left Haar measure is also right invariant.)

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We know its connected component $SO(2)$ is unimodular because it’s Abelian. And there is a result says for a connected Lie group, it is unimodular if it is compact or reductive. But this provided with the assumption that $G$ is connected.

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I guess $O(2)$ is unimodular indeed. But how to give a proof ?