No. If the other number is negative,
then the product is positive.
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27 multiplied by any negative number will give a negative product of 27.
It is negative.
The product of zero and any number is always 0.
It is positive. Any product of an even number of negative numbers will be positive, regardless of how many positive numbers you have. Similarly any product of an odd number of negative numbers will be negative, regardless of how many positive numbers you have.
If there is any zero in the set of integers, their product is zero.If there is an odd number of negative integers, then the product is negative, whereas if there is an even number of negative values, the product is positive.