Ellipsis omits words already clear from context (She can sing, and her sister can too). Substitution replaces them with a pro-form: so/not for clauses (I think so), do so for verb phrases, and so/neither + auxiliary for agreement (So do I / Neither did she). These are markers of advanced, fluent English.
We use 'so + auxiliary + subject' (positive) and 'neither/nor + auxiliary + subject' (negative) to avoid repeating a verb phrase. Choose the correct form.