Answer
$\left|\begin{array}{cc}-7 / 2 & 5 / 2 \\ 3 & -2\end{array}\right|$
Work Step by Step
Inverse of inverse of $C$ is $C .$ So, to find $C$ we should get $\left(C^{-1}\right)^{-1}$.
Use formula for inverse of $2 \times 2$ matrix.
If $A=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right],$ then $A^{-1}=\frac{1}{a d-b c}\left[\begin{array}{cc}d & -b \\ -c & a\end{array}\right]$
$\left|\begin{array}{cc}4 & 5 \\ 6 & 7\end{array}\right|^{-1}=\frac{1}{28-30}\left|\begin{array}{cc}7 & -5 \\ -6 & 4\end{array}\right|=\left|\begin{array}{cc}-7 / 2 & 5 / 2 \\ 3 & -2\end{array}\right|$
