Just to expand (or confuse?) the answer further, both word orders can actually be used and it really depends on the intended emphasis and contextual meaning.
"Ne, Matěj jsem já." and "Ne, já jsem Matěj." are both valid, but the emphasis is different.
In the first sentence, the emphasis is on "já". In the second sentence, the emphasis is probably on "Matěj", although you could put it on "já" with intonation to get the same contextual meaning as the first sentence.
The emphasis on "já" would give you the sense that Balaovic described. The emphasis on "Matěj" could be used e.g if somebody asked if you are Jakub.
There are no reversed positions in negative sentences, it's meaning that's different: Compare: A- Kdo jsi? (Who are you?) B- Já jsem Matěj. (I am Matěj.) ---> question- you don't know the answer
A- On je Matěj? (He is Matěj?) B- Ne, Matěj jsem já! (No, I am Matěj!) ----> question- you think, you know the answer but wanna be sure ---->answer- "No, he's NOT Matěj, I am Matěj, I am Matěj- so please, REMEMBER IT!!!"