Which of the following represents the inverse of the matrix below? A=beginbmatrix a&b c&dendbmatrix

A^{-1} = \begin{bmatrix}- \dfrac{\dfrac{\left(\overline{a} b + \overline{c} d\right) \left(- \dfrac{\overline{a} \left(a \overline{b} + c \overline{d}\right)}{a \overline{a} + c \overline{c}} + \overline{b}\right) \overline{\dfrac{1}{\sqrt{a \overline{a} + c \overline{c}}}}}{\sqrt{- \dfrac{\left(a \overline{b} + c \overline{d}\right) \left(\overline{a} b + \overline{c} d\right) \overline{\dfrac{1}{\sqrt{a \overline{a} + c \overline{c}}}}}{\sqrt{a \overline{a} + c \overline{c}}} + b \overline{b} + d \overline{d}} \overline{\sqrt{- \dfrac{\left(a \overline{b} + c \overline{d}\right) \left(\overline{a} b + \overline{c} d\right) \overline{\dfrac{1}{\sqrt{a \overline{a} + c \overline{c}}}}}{\sqrt{a \overline{a} + c \overline{c}}} + b \overline{b} + d \overline{d}}}} - \dfrac{\overline{a}}{\sqrt{a \overline{a} + c \overline{c}}}}{\overline{\sqrt{a \overline{a} + c \overline{c}}}} & - \dfrac{\dfrac{\left(\overline{a} b + \overline{c} d\right) \left(- \dfrac{\left(a \overline{b} + c \overline{d}\right) \overline{c}}{a \overline{a} + c \overline{c}} + \overline{d}\right) \overline{\dfrac{1}{\sqrt{a \overline{a} + c \overline{c}}}}}{\sqrt{- \dfrac{\left(a \overline{b} + c \overline{d}\right) \left(\overline{a} b + \overline{c} d\right) \overline{\dfrac{1}{\sqrt{a \overline{a} + c \overline{c}}}}}{\sqrt{a \overline{a} + c \overline{c}}} + b \overline{b} + d \overline{d}} \overline{\sqrt{- \dfrac{\left(a \overline{b} + c \overline{d}\right) \left(\overline{a} b + \overline{c} d\right) \overline{\dfrac{1}{\sqrt{a \overline{a} + c \overline{c}}}}}{\sqrt{a \overline{a} + c \overline{c}}} + b \overline{b} + d \overline{d}}}} - \dfrac{\overline{c}}{\sqrt{a \overline{a} + c \overline{c}}}}{\overline{\sqrt{a \overline{a} + c \overline{c}}}}\\\dfrac{\left(a \overline{a} + c \overline{c}\right) \overline{b} - \overline{a} \left(a \overline{b} + c \overline{d}\right)}{\sqrt{\dfrac{\sqrt{a \overline{a} + c \overline{c}} \left(b \overline{b} + d \overline{d}\right) - \left(a \overline{b} + c \overline{d}\right) \left(\overline{a} b + \overline{c} d\right) \overline{\dfrac{1}{\sqrt{a \overline{a} + c \overline{c}}}}}{\sqrt{a \overline{a} + c \overline{c}}}} \overline{\sqrt{\dfrac{\sqrt{a \overline{a} + c \overline{c}} \left(b \overline{b} + d \overline{d}\right) - \left(a \overline{b} + c \overline{d}\right) \left(\overline{a} b + \overline{c} d\right) \overline{\dfrac{1}{\sqrt{a \overline{a} + c \overline{c}}}}}{\sqrt{a \overline{a} + c \overline{c}}}}} \left(a \overline{a} + c \overline{c}\right)} & \dfrac{- \left(a \overline{b} + c \overline{d}\right) \overline{c} + \left(a \overline{a} + c \overline{c}\right) \overline{d}}{\sqrt{\dfrac{\sqrt{a \overline{a} + c \overline{c}} \left(b \overline{b} + d \overline{d}\right) - \left(a \overline{b} + c \overline{d}\right) \left(\overline{a} b + \overline{c} d\right) \overline{\dfrac{1}{\sqrt{a \overline{a} + c \overline{c}}}}}{\sqrt{a \overline{a} + c \overline{c}}}} \overline{\sqrt{\dfrac{\sqrt{a \overline{a} + c \overline{c}} \left(b \overline{b} + d \overline{d}\right) - \left(a \overline{b} + c \overline{d}\right) \left(\overline{a} b + \overline{c} d\right) \overline{\dfrac{1}{\sqrt{a \overline{a} + c \overline{c}}}}}{\sqrt{a \overline{a} + c \overline{c}}}}} \left(a \overline{a} + c \overline{c}\right)}\end{bmatrix}