The prime numbers are the numbers that are only divisible by 1 and themselves. In this question, we are asked to find the prime numbers between 10 and 100 that remain prime when their digits are reversed.

To solve this problem, we can start by listing all the two-digit prime numbers between 10 and 100. Then, we will check if each of these primes remains prime when the order of their digits is reversed.

Listing the two-digit prime numbers between 10 and 100:
- 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

Checking if the reverse of each number is also prime:
- 11: The reverse is 11, which is prime.
- 13: The reverse is 31, which is prime.
- 17: The reverse is 71, which is prime.
- 19: The reverse is 91, which is not prime.
- 23: The reverse is 32, which is prime.
- 29: The reverse is 92, which is not prime.
- 31: The reverse is 13, which is prime.
- 37: The reverse is 73, which is prime.
- 41: The reverse is 14, which is not prime.
- 43: The reverse is 34, which is prime.
- 47: The reverse is 74, which is not prime.
- 53: The reverse is 35, which is prime.
- 59: The reverse is 95, which is not prime.
- 61: The reverse is 16, which is not prime.
- 67: The reverse is 76, which is not prime.
- 71: The reverse is 17, which is prime.
- 73: The reverse is 37, which is prime.
- 79: The reverse is 97, which is prime.
- 83: The reverse is 38, which is prime.
- 89: The reverse is 98, which is not prime.
- 97: The reverse is 79, which is prime.

From the above analysis, we can see that there are 9 prime numbers between 10 and 100 that remain prime when their digits are reversed. Therefore, the correct answer is option 'B' - 9.

Prime numbers from 10 to 100 that remain prime even after their digits are reversed are 11, 13, 17, 31, 37, 71, 73, 79 and 97.