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????