What location in the earth has the same latitude as norway but in the opposite hemisphere (either north or south)?

Norway is located around 60°N - and more, also around 65°N.

So we're looking for a place located 60°S or 65°S.

No land crosses the 60°S exactly, but some uninhabited Islands lie close to it.

65°S crosses Antarctica. - so the best answer is Antarctica. (since  you didn't specify longitude,   I think this answer is enough and you don't need more specific answer but let me know if you do)

Answer (true);