Correct Option: B

As we know from the formula,
A³ + B³ + C³ = ( A + B + C) (A² + B² + C² – AB – BC – CA) + 3ABC
If A + B + C = 0 then,
A³ + B³ + C³ = 0 x (A² + B² + B² – AB – BC – CA) + 3ABC
A³ + B³ + C³ = 0 + 3ABC
A³ + B³ + C³ - 3ABC= 0
As we know that from given question,
A = a, B = b and C = 1, Put these value in above equation, we will get
a³ + b³ + 1³ - 3 x a x b x 1 = 0
a³ + b³ + 1 - 3ab = 0