题目内容

设S=Q×Q,其中Q为有理数集合,定义S上的二元运算 * ,
<a,b>,<x,y>∈S有<a,b> * <x,y>=<ax,ay+b>则下面说法中,正确的是
Ⅰ.S上的二元运算 * 是可交换的
Ⅱ.S上的二元运算 * 是可结合的
Ⅲ.* 运算存在单位元
Ⅳ.* 存在零元

A. Ⅰ和Ⅱ
B. Ⅰ、Ⅱ和Ⅲ
C. Ⅲ和Ⅳ
D. Ⅱ和Ⅲ

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