According to the wikipedia article on this word, it is composed of αὐτός and ματος, which seems to be derived from "the proto-Indo-European *méntis ~ *mn̥téys (“thought”)."
My question is simple: Is there in Attic Greek such a word as ματος, considered on its own?
There is no independent word ματος in any form of Greek we know of or can reconstruct; it's often the case that forms found in compounds are not found as independent words with the exact same shape. But there are many Greek words which come from the same Indo-European root. For example:
From the same root we get Latin mens "mind", as well as the English word mind itself.
The answer to your question is no. *matos does not exist as a word on its own in any Greek dialect. But it can confidently be posited for proto-Greek, where it is cognate of Latin -mentus. *mato- is the expected Greek representative of IE *mnto-.
