Use the given information to find A. $$   (-2A^{-1}-I) ^T = \begin{bmatrix}
        1 & -2 \\
        -4 & 7 \\
        \end{bmatrix}
$$
I did it like this:
$$   -2A^{-1}-I = \begin{bmatrix}
        1 & -4 \\
        -2 & 7 \\
        \end{bmatrix}
$$
=     $\dfrac{1}{(1)(7)-(-4)(-2)}$
Did I start the problem correctly? Any help is very much appreciated!

First find $A^{-1}$ from the given equality
$$A^{-1}=-\frac12\left(I+\begin{bmatrix}
        1 & -2 \\
        -4 & 7 \\
        \end{bmatrix}^T\right)=\begin{bmatrix}
        -1 & 2 \\
        1 & -4 \\
        \end{bmatrix}$$
and then invert this matrix to find
$$A=\frac12\begin{bmatrix}
        -4 & -2 \\
        -1& -1 \\
        \end{bmatrix}$$
