what does it mean by integer/ m integer?
im asked to find all the units of integer/ 12 integer and im not sure what does that mean.
thanks
I'm not certain what you mean by "integer/12 integer" but I suspect you mean , the "integers modulo 12". The "units of a ring" are those members of ring that have a multiplicative inverse. It should be easy to see that if a number has a common factor with 12, then some multiple of it will be a multiple of 12, so congruent to 0 modulo 12, so cannot have a multiplicative inverse.
More to the point, [2] does not have an inverse (and so is not a unit) because [2][6]= [0]. Of course, that is a direct result of the fact that gcd(2, 12)= 2 not 1.
[5], [7], and [11] are units but you are missing one obvious one. Remember that the set of all units of a ring form a group with multiplication.