I believe both A. and B. are correct and, as RonBee pointed out, tend to be used as synonyms by some speakers.
The word 'sorry', as jwschang rightly adds, isn't a 'verb', but rather an adjective: it describes a state of being: "be sorry".
Technically, 'sorry about' is comprised of two separate units: an adjective and a preposition, whereas 'sorry for' has two different structures:
1) a phrasal adjective: one unit comprised of an adjective plus a preposition, and
2) two separate units: an ajdective plus a preposition.
As a phrasal adjective, 'sorry for' expresses
a different meaning from 'sorry about':
sorry about X
[adj] + [prep]
with regards to X
sorry for X
[adj + prep]
sympathy towards X
Examples:
1. I am sorry
about the noise. (feel sorry regarding the noise)
2. I am sorry
for the noise. (feel pity towards the noise)
Ungrammatical
3. I am sorry
for her. (feel pity towards her)
It's only when 'sorry for' is expressed as two separate units, that it shares a similar meaning to 'sorry about':
'sorry for' and 'sorry about' as
synonyms:
sorry for X
[adj] + [prep]
in reference to X
sorry about X
[adj] + [prep]
with regards to X
3. I am sorry
for the noise. (with reference to)
grammatical
4. I am sorry
about the noise. (with regards to)
grammatical
Cas
