设 $\mathrm{A}$ 为 2 阶可逆矩阵, 且 $(2 A)^{-1}=\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right]$, 则 $\mathrm{A}=$
$ \text{A.}$ $\frac{1}{2}\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right]^{-1}$
$ \text{B.}$ $2\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right]^{-1}$
$ \text{C.}$ $\frac{1}{2}\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right]$
$ \text{D.}$ $2\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right]$