One who is unrelenting and cannot be moved by entreaties

Answer: Option A

One word substitute is Inexorable.

Inexorable: (of a person) impossible to persuade; unrelenting.
Infallible: incapable of making mistakes or being wrong.
Impregnable: (of a fortified position) unable to be captured or broken into.
Inexplicable: unable to be explained or accounted for.