Who killed Jimmy?

Logic Level 1

Three suspects appeared in court for the crime of murdering Jimmy. Exactly one of them is the murderer.

The judge asked the following question: "Did the murderer currently have black or brown hair?"

Alice (Female with black hair): "She has black hair."
Andrew (Male with black hair): "Alice is lying! She has brown hair."
Anna (Female with brown hair): "I speak the truth! He has brown hair."

Given that only one of them is telling the truth, any sentence a liar states is a lie, and no one accuses themselves, who is telling the truth?

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