(3) Let p be an odd prime number. Which integers a have the property that the inverse of a is congruent to a modulo p? Study the case p = 7 and p = 11 first. Reorder the factors in (p-1)! in such a way that all pairs of inverses are written adjacent to one another. Compute (p-1)! modulo p after this reordering. What is (p-1)! mod p.