Modular arithmetic

If it is asked to find (C^(-1))%M then how should we proceed.

C-1 % m = Cm-2%m simple

in python -

m = 10**9 +7
c = int(input())
ans = pow(c,m-2,m)

But why is it so. I mean the expression dosent indicates us to find modular multiplicative inverse. It simply seems to be 1/C mod M.

google : a inverse mod m gfg