To understand this problem, let's break it down step by step:

Given:
- Set A has 99 elements in common with Set B.

We need to find:
- The number of elements common to each of the sets A x B and B x A.

Breaking it down:

A x B represents the Cartesian product of sets A and B.
- In the Cartesian product of two sets, each element of the first set is paired with each element of the second set.

B x A represents the Cartesian product of sets B and A.
- Similarly, in the Cartesian product of two sets, each element of the first set is paired with each element of the second set.

Now, let's consider the number of elements common to A x B and B x A.

The number of elements in A x B can be determined by multiplying the number of elements in set A by the number of elements in set B. Similarly, the number of elements in B x A can be determined by multiplying the number of elements in set B by the number of elements in set A.

Since set A and set B have 99 elements in common, when we calculate the number of elements in A x B and B x A, these 99 common elements will be counted twice.

Therefore, the number of elements common to each of the sets A x B and B x A will be the total number of elements in A x B minus the 99 common elements.

The formula to calculate the number of elements in A x B is:
Number of elements in A x B = Number of elements in set A * Number of elements in set B

Similarly, the formula to calculate the number of elements in B x A is:
Number of elements in B x A = Number of elements in set B * Number of elements in set A

Since A x B and B x A have the same number of elements, we can use either formula to calculate the total number of elements common to both sets.

Calculating the number of elements common to each of the sets A x B and B x A:
Number of elements common to A x B and B x A = Number of elements in A x B - 99 (common elements)

Hence, the correct answer is option 'B' (992).