I've tried a problem for a very long time but I can't seem to get it right (my answer is different from the one in my textbook).
Could you please tell me where I went wrong?
Thank you!
Your inverse matrix is incorrect. You have correctly calculated the determinant but you also need to swap two entries and negate the other two.
$\displaystyle
\frac{-1}{106}\left[\begin{array} {cc} -10&-8 \\ -7&5 \end{array}\right]
\left[\begin{array} {cc} 5&8 \\ 7&-10 \end{array}\right]=
\left[\begin{array} {cc} 1&0 \\ 0&1 \end{array}\right]
$