Question 486936
In a question like this you need to be specific while talking about inverses it might be additive inverses or multiplicative inverses. But I will try to explain while multiplicative inverses does not exist in some cases. the identity element is 1. consider 2x7, you will get 14 which under modulo 13 gives 1 hence 2 is the inverse of7.   consider 22x8 which gives 176 and so 1 under modulo 1 so, 22 is the inverse of 8 under modulo 35. Also consider 67x3 which also gives 1 under modulo 100. The inverse actually exist  only if the number and the modulo are relatively prime i.e no commom factors consider 15mod18, 15 and 18 has 3 as a common factor so 15 can never have any inverse under mod 18. Try the remaining then I will see to them if you can't handle them