Okay, Correct me if I'm wrong, but the two question are

Let p be prime.

1) If and (mod p) then (mod p)

2) (mod p)

For 1 we get

(mod p)

(mod p)

(mod p)

or

(mod p) or (mod p)

(mod p)

2) is wrong. The correct version is (mod p), the result is known as Wilson's Theorem

Now 1 and p-1 are the only numbers modulo p that are their own inverses.

For any other number x such that there exists such that and (mod p).

So we match up each x with its inverse and we get:

(mod p)

Now we have the desired result.