How to prove (p-1) = -1 (mod p), p is a prime.

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(p-1)! = -1(mod p), where p is a prime
I have tried small values of p but I can't find any pattern. Can anyone give me some hints or directions? I don't know a detail proof. Thank you
 
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The matter turns on inverses. For every a in the system there is an a^-1, such that a*a^-1 = 1. (Generally that is an axiom of the group property.)
 

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