Ideals and quotient rings

Below you find the addition and multiplication table of the ring R = Z/3Z ×Z/4Z.

With the help of the generate button you can construct ideals of this ring.

Consider the ideal I generated by (0,2). Color all the distinct residue classes with different colors. Cna you read of the multiplication table of R/I? Is it a domain or field?

How about the case when the idealI is generated by (1,0)? Or by both (1,0) and (0,2)?