IMO : B

Statement 1: 0< b< 1

if b lies in 0< b< 1 then
a can lie in 0< a< 1 or -1 < a< 0.
For eg: if b = 1/4 then a can be 1/2 or -1/2 .
Not suff

Statement 2: a > b
Given \(a^2 = b\) i.e b >=0. And if a>b then a must also be >=0
If a>b then
for a>1 then \(a^2 > b\). They cannot be equal
so a must be in interval 0<a<1

PS: a cannot be equal to "0" or "1" since it violates the statement 2: a>b

800score Official Solution:

Statement (1) tells us that b is between 0 and 1, so we also know that a² is between 0 and 1 since b = a². If a is any number between -1 and 1, then a² will be
between 0 and 1, so Statement (1) is insufficient.

Statement (2) tells us that a > b, and since a² = b, we know that a > a². This is only true for
numbers between 0 and 1. The square of any number that is larger than 1 or negative will be larger than the number itself. So Statement (2) is sufficient.

Since Statement (1) is insufficient and Statement (2) is sufficient, the correct answer is choice (B).
_________________