You need an identity to solve this!
99² = (100-1)²
(Using Identity) (a-b)²= a²-2ab+b²
(100)²-2(100)(1)+(1)²
= 10000-200+1
= 10001-200
= 9801

Therefore, option A is the correct answer!

Identity:
The identity that can be used to evaluate the given expression is (a + b)(a - b) = a^2 - b^2.

Explanation:
To evaluate the given expressions, we can use the identity (a + b)(a - b) = a^2 - b^2. This identity states that the product of the sum and difference of two numbers is equal to the difference of their squares.

Evaluating the expressions:

a) 9801:
To evaluate 9801, we can rewrite it as 100^2 - 1^2. So, a = 100 and b = 1.
Using the identity, we have (a + b)(a - b) = a^2 - b^2.
Substituting the values, we get (100 + 1)(100 - 1) = 100^2 - 1^2.
Simplifying further, (101)(99) = 10000 - 1.
Therefore, 9801 is equal to 10000 - 1, which is the correct answer.

b) 10199:
To evaluate 10199, we can rewrite it as 102^2 - 1^2. So, a = 102 and b = 1.
Using the identity, we have (a + b)(a - b) = a^2 - b^2.
Substituting the values, we get (102 + 1)(102 - 1) = 102^2 - 1^2.
Simplifying further, (103)(101) ≠ 102^2 - 1.
Therefore, 10199 is not equal to 102^2 - 1.

c) 10201:
To evaluate 10201, we can rewrite it as 101^2 - 1^2. So, a = 101 and b = 1.
Using the identity, we have (a + b)(a - b) = a^2 - b^2.
Substituting the values, we get (101 + 1)(101 - 1) = 101^2 - 1^2.
Simplifying further, (102)(100) ≠ 101^2 - 1.
Therefore, 10201 is not equal to 101^2 - 1.

d) 10001:
To evaluate 10001, we can rewrite it as 101^2 - 1^2. So, a = 101 and b = 1.
Using the identity, we have (a + b)(a - b) = a^2 - b^2.
Substituting the values, we get (101 + 1)(101 - 1) = 101^2 - 1^2.
Simplifying further, (102)(100) ≠ 101^2 - 1.
Therefore, 10001 is not equal to 101^2 - 1.

Conclusion:
Out of the given options, only 9801 can be evaluated using the identity (a + b)(a - b) = a^2 - b^2. The remaining options do not satisfy this identity.