$$\left[\begin{matrix} 5 & 1 & 3 \\1 & 2 & -3 \\5 & -2 & 3 \end{matrix}\right]$$
$-54$
$\left(\begin{matrix}5&1&3\\1&2&-3\\5&-2&3\end{matrix}\right)$
$\left(\begin{matrix}0&\frac{1}{6}&\frac{1}{6}\\\frac{1}{3}&0&-\frac{1}{3}\\\frac{2}{9}&-\frac{5}{18}&-\frac{1}{6}\end{matrix}\right)$
$10$
$\left(\begin{matrix}5&1&5\\1&2&-2\\3&-3&3\end{matrix}\right)$
$3,3$
$\left(\begin{matrix}1&0&0\\0&1&0\\0&0&1\end{matrix}\right)$
$\left[\begin{array}{rrr}0 & -9 & -9 \\ -18 & 0 & 18 \\ -12 & 15 & 9\end{array}\right]$