Assignment:
Let g(x) = x2 + x -1 and let h(x) = x3 - x + 1. Obtain fields of 4, 8,9 and 27 elements by adjoining a root of f (x) to the field F where f (x) = g(x) or h(x) and F = F2 or F3. Write down the multiplication tables for the fields with 4 and 9 elements and show that the nonzero elements form a cyclic group.
Provide complete and step by step solution for the question and show calculations and use formulas.