The question on whether to use singular or plural verbs is a rather complex one here, actually. Generally, 'neither' is used with a singular verb:
"Do not attempt to bring livestock or plant material into the country; neither IS permitted."
In colloquial English, however, it's perfectly legit to say "neither ARE permitted."
When neither is followed by "of," it's common to use a plural verb. In your case:
"Neither of the answers ARE correct."
But for formal writing, use a singular verb still. So, formally, you get:
"Neither of the answers IS correct."