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Q: Asking for assistance in understanding and solving this example on Modern Algebra II with the steps of the solution to better understand, thanks.

**Please give the step by steps with details to completely see how the solution came about.

1) Determine all elements in an integral domain that are their own inverses under multiplication.

2) Let F be a finite field with n elements. Prove that x^(n-1 )= 1 for all nonzero x in F. Hint: Use the fact that the nonzero elements of F form a group under the multiplication operation.

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