We have because 7 - (-5) is a multiple of 12 (or, 7 = -5 + 12). On the other hand, . So indeed, .
I am using euclidean algorithm to find if 7 inverse exists in mod12
I ended up with
1=3(12)-5(7)
So the inverse of 7 is -5
and this is what the instructor wrote in the notes but he went from
7^-1=5(mod12)
to
7^-1=7(mod12)
what happened here and how did he end up with 7 inverse being 7 in the field of mod12????