对于实数a、b、c，下列命题中正确的是（　　）

A：$\left.\begin{array}{c}a+b>4\\ a·b>4\end{array}\right\}\Rightarrow \left\{\begin{array}{c}a>2\\ b>2\end{array}\right.$

B：$\left.\begin{array}{c}a>b\\ a\ne 0,b\ne 0\end{array}\right\}\Rightarrow \frac{1}{a}<\frac{1}{b}$

C：$a>b\Rightarrow a{c}^2>b{c}^2$

D：$a<b<0\Rightarrow \frac{b}{a}<\frac{a}{b}$