If A and B are two non-empty sets having 10 elements in common, then how many elements do A\times B and B\times A have in common?

Explanation

The intersection of two Cartesian products satisfies the property (A \times B) \cap (B \times A) = (A \cap B) \times (B \cap A). Since sets A and B have 10 elements in common, the number of common elements in their Cartesian products is 10 \times 10 = 100.

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