1. Suppose there are two propositions;

甲: $a$ is a real number greater than zero; 乙: $a>b$ and $a^{-1}>b^{-1}$, then
(A) 甲 is a sufficient but not necessary condition for 乙;
(B) 甲 is a necessary but not sufficient condition for 乙;
(C) 甲 is a sufficient and necessary condition for 乙;
(D) 甲 is neither a sufficient condition nor a necessary condition for 乙.
1. (B)

Since when "甲" is established, "乙" is not necessarily established (for example, when $a=3, b=2$, 甲 is established, but 乙 is not established), it can be known that "甲" is not a sufficient condition for "乙".

Next, let's look at when "乙" is established. It is obvious that "乙" can only be established when and only when $a>0$ and $b<0$. Therefore, it can be known that "甲" is a necessary condition for "乙" to be established. In summary, "甲" is a necessary but not sufficient condition for "乙".