Consider Z4 ({0, 1, 2, 3} mod 4) and GF (4) (also known as GF(2^2)).

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(a) Is (Z4, +) a group? Is (Z4, +, *) a ring? Explain.
(b) Is Z4 a field, in other words, does every integer in Z4 have a multiplicative inverse?
(c) Generate the addition table and multiplication table of GF(4).

can someone help me. i am clueless?
 
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Have you had any thoughts on the problem?
 
In particular, have you written out the addition and multiplication tables for Z4?
 
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