Final answer:
The correct sentence with subject-verb agreement is 'She has written several books about physics,' where both the subject and verb are singular.
Step-by-step explanation:
The sentence that shows correct subject-verb agreement is: c. She has written several books about physics. Here, the subject 'She' which is singular agrees with the verb 'has written', which is also in its singular form. In option a, 'A scientist' is singular, but the verb 'gain' should be 'gains' to match in number. In option b, 'The inventor' is singular, so 'are' should be 'is' to agree with the singular subject. The pronoun 'She' refers to a singular person, and the verb 'has written' also indicates a singular action.