1. Suppose there are two propositions, A: $a$ is a real number greater than zero; B: $a>b$ and $a^{-1}>b^{-1}$, then
A. A is a sufficient but not necessary condition for B
B. A is a necessary but not sufficient condition for B
C. A is a sufficient and necessary condition for B
D. A is neither a sufficient condition nor a necessary condition for B
Given $a>b$ and $a^{-1}>b^{-1} \Rightarrow a>0, b<0$, thus Beta $\Rightarrow$ Alpha, Alpha $\nRightarrow$ Beta. Therefore, the answer is $B$.

