Is the Hadith "If he greets, he greets three times, and if he speaks a word, he repeats it three times" authentic? And what is the response to those who describe the one who does so as abnormal, if it is authentic?

It was authentically reported from the Prophet, peace and blessings be upon him, that when he spoke a word, he would repeat it three times so that it would be understood from him. And when he greeted a people, he would greet them three times. This is due to his excellent teaching and his eagerness to make his Ummah understand. The repetition of the greeting may be for seeking permission, or for giving salutations of greeting and farewell, or for fear that his words might not be heard, or due to the large gathering.