已知矩阵 $A$的逆矩阵 $A^{-1}=\left[\begin{array}{c}-\frac{1}{4}\\ \frac{1}{2}\end{array}\begin{array}{c}\frac{3}{4}\\ -\frac{1}{2}\end{array}\right]$，求矩阵 $A$的特征值．