Thread: Integers modulo n

prove or disprove that Z_3 and Z_4 is a group with respect to (*)?
where operation (*) on Z_n is associative and commutative and has [1] as an identity element.

Originally Posted by Vedicmaths

prove or disprove that Z_3 and Z_4 is a group with respect to (*)?
where operation (*) on Z_n is associative and commutative and has [1] as an identity element.

Z_3 is a group because everything is invertible. Z_4 is not, because 2 has no inverse.