Do you want to find a multiplicative inverse for all numbers from 1 to N — 1?

It can be easily done for a prime N, the idea should be obvious if you'll read about primitive roots modulo N.

For non-prime N the idea should also be similar.

if the number with respect to which you are finding the modular inverse (i.e. the 'M' in A%M is prime)you can use the Fermat's little theorem according to which the modular inverse of a number with respect to a prime number (say A and P respectively) is pow(A,P-2)

so in one for loop you may find the modular multiplicative inverses of the numbers in the range but the complexity is O(nlogp) as the power function takes log(p) time

http://e-maxx.ru/algo/reverse_element#4 (it's in russian but you can see the code)