hello!
In order to find the reciprocal of a number, we should just flop it over, like so:-

Flop it over:-

There's something you should notice about this number.
No matter how we flop it over, we're going to end up with -1.
Hence, the reciprocal of -1 is:-

note:-
Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I'll comment and/or edit my answer :)