statement 1.
a = b -1 ==> a[(a+1)^2] = (b -1)(b)^2
It depends on value of a or b so, st1 is not sufficient.

Statement2.
a = (b^2) - 1 ==> a(b)^2 = a(a +1) = ((b)^2 + 1)((b)^2)
Again it depends on value of a or b so, st2 is also not sufficient.

consider both together.
a = b - 1 --- (1)
a = b^2 -1 = (b -1)(b + 1) ----(2)
from eq (1) and (2)
(b-1)b = 0 ==> b = 0 or 1 .
if b = 0 then a = -1 ==> a(b)^2 = 0
if b = 1 then a = 0 ==> a(b)^2 = 0
Hence together are sufficient.
Ans should be C