Because the opposite of 8 for example is -8 and 8+(-8) = 0
Because that is how the opposite is defined!
When the number is 0.
the number 0 is always equal to its opposite
When the number is non-positive.
No. If the rational number is not zero, then such a product is irrational.
Yes, it will always be irrational.
The answer depends on whether the "opposite" means the multiplicative inverse or the additive inverse.
Yes, except in the degenerate case where the rational number is 0, in which case the product is also 0, a rational result.
The product of 0 and an irrational is 0 (a rational), the product of a non-zero rational and any irrational is always irrational.
Think of a numberline, Travle 5 sides to the negative side, and than 5 steps back , this is negative 5 and positive 5. This appplies for all rational numbers
Only if the rational number is 0.