why prime numbers do not have multiplicative and additive inverse?
Prime numbers have both multiplicative and additive inverses - the multiplicative inverse is the reciprocal and the additive inverse is the number which when added to a number, any number, an integer which is prime;say 7, gives zero, so the multiplicative inverse of 7 is 1/7 and it's additive inverse is -7, because 7+(-7) 0.
So why does Shanali get a down thumb and Ray gets an up thumb? They both said the same thing, except Ray followed suit and said it two minutes later. No one has ever told you that prime numbers didnt have multiplicative or additive inverses. You made that up or you grossly misunderstood some subject matter far too far outside of your grasp to comprehend. If you meant to ask, why dont prime numbers have integer-valued multiplicative or additive inverses then the answer is no number besides 1 does. Even the composite number 10 follows the same pattern. I dont see where you even got the material from which to formulate this question.
Prime numbers DO have multiplicative and additive inverses. For example: 7 is a prime number. 1/7 is its multiplicative inverse . because 7*(1/7) 1 -7 is its additive inverse . because 7 + (-7) 0 _______________________________