Final answer:
The question is about a list of numbers that always have a product of zero when any two are multiplied. This implies that all numbers in the list must be zero, as a zero product requires at least one of the multipliers to be zero.
Step-by-step explanation:
The question pertains to determining whether all numbers in a list are equal to zero given that the product of any two numbers in the list is equal to zero. If the product of any two numbers is zero, this implies that at least one of the numbers involved in each multiplication operation must be zero. For there to be more than two numbers in the list, and for their product to always be zero, this would mean that all numbers in the list must be zero.
If there was a non-zero number in the list, multiplying it by any other number would produce a non-zero product unless the other number is zero. However, since the condition specifies that any two numbers from the list when multiplied result in a product of zero, the only possibility is that every number in the list is zero.
It is important to remember rules of multiplication such as: when two positive numbers multiply, they produce a positive result; similarly, two negative numbers also produce a positive result. A zero product implies that one or both multipliers must be zero.