6・1 Suppose there are two propositions:
Proposition A: $a$ is a real number greater than 0. Proposition 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.
(China High School Mathematics Competition, 1985)
[Solution] Let $a>b, a^{-1}>b^{-1}$, then it must be that $a>0$ (in fact, if $ab$ there is $bb$, but $a^{-1}<b^{-1}$, which means that condition 甲 is not a sufficient condition for 乙.
Therefore, the answer is $(B)$.