What defining characteristic applies to the associative property of multiplication?

The associative property of multiplication states that the way in which numbers are grouped in a multiplication problem does not affect the product. This means that when you multiply three or more numbers, changing the grouping of those numbers will yield the same result. For example, if you have three numbers—let's say 2, 3, and 4—you can group them differently: (2 x 3) x 4 = 6 x 4 = 24, or you could group them as 2 x (3 x 4) = 2 x 12 = 24. In both cases, the product remains 24, illustrating the associative property.

The other scenarios presented don't align with the definition of the associative property. The idea that the product of numbers changes with grouping does not apply in this context, as the associative property specifically states that the product remains constant. The concept of a product always being zero relates more to multiplication involving the number zero, which is not relevant here. Lastly, the notion that the order of numbers affects the product describes the commutative property rather than the associative property.