6,7. please help, just single choice questions, no need for any explanations

(6) Which one is false among the following four statements? 1 A. A field must be an integral ring. B. An integral ring must be a ring without zero divisor. C. Complex number ring C is a field. D. Z12 with respect to addition modula 12 forms an integral ring. (7) Let G be a group, and a,b and c be three finite-order elements of G. Which one is false among the following choices? ( ) A. If ab=ac, then b=c. B. (ab)1=b1a1. C. There must be an element xG, such that G=x. D. G must have at least one subgroup