The assertion in the question is simply not true.
The product of two mixed numbers is always greater than one (assuming that both of the mixed numbers themselves are greater than one.)
Not always, but most of the time.
The product will be greater than 1, when each of the two factors are greater than 1.
The product of two digit numbers is always greater than either.
No. Their product is always greater than 0.
Whenever you multiply two negative real numbers.
Yes, if both the numbers have the same sign. But not if only one of them is negative.
If ever you have an odd number of negative numbers, the product will always be a negative number. So the answer to this question is negative.