[SOLVED] Math 231 — hw 2

1. Today we looked at an example of a finite field, a field with finitely many objects:
Zp. TSuch structures are always fields when p is a prime number. For Z5, find all the
additive and multiplicative inverse of the elements in the field: {0, 1, 2, 3, 4}. (Note
that 0 will have no multiplicative inverse.)
2. For finite fields, p must be a prime number. To illustrate why Z4 is not a field, construct
its multiplication table.
Recall that a multiplication table is a table where the header row and first column list
the elements of the set, and each cell contains the product of the corresponding row
and column elements.