Exercise 2.7.1

$A=\left[\begin{array}{cc}1\hfill & 0\hfill \\ 9\hfill & 3\hfill \end{array}\right]$has $A^T=\left[\begin{array}{cc}1\hfill & 9\hfill \\ 0\hfill & 3\hfill \end{array}\right],A^{-1}=\left[\begin{array}{cc}\hfill 1\hfill & \hfill 0\hfill \\ \hfill -3\hfill & \hfill 1∕3\hfill \end{array}\right],{\left(A^{-1}\right)}^T={\left(A^T\right)}^{-1}=$ $\left[\begin{array}{cc}\hfill 1\hfill & \hfill -3\hfill \\ \hfill 0\hfill & \hfill 1∕3\hfill \end{array}\right];$ $A=\left[\begin{array}{cc}1\hfill & c\hfill \\ c\hfill & 0\hfill \end{array}\right]$has $A^T=A$ and $A^{-1}=\frac{1}{c^2}\left[\begin{array}{cc}0\hfill & c\hfill \\ c\hfill & -1\hfill \end{array}\right]={\left(A^{-1}\right)}^T.$