9. Yes

11. Yes

13. No

15. No

17. Yes

19. $A^{-1}=\left[\begin{array}{rr}{\displaystyle \frac{1}{2}}& 0\\ -{\displaystyle \frac{1}{6}}& {\displaystyle \frac{1}{3}}\end{array}\right]$

21. Does not exist

23. $A^{-1}=\left[\begin{array}{rrr}1& -8& 10\\ 0& 2& -3\\ 0& -1& 2\end{array}\right]$

25. $A^{-1}=\left[\begin{array}{rrr}1& 1& -1\\ -1& 1& 0\\ 2& -5& 2\end{array}\right]$

27. $\left[\begin{array}{rrr}1& -1& 0\\ -2& 3& -4\\ -2& 3& -3\end{array}\right]$

29. $A^{-1}=\left[\begin{array}{rr}1& 0\\ -{\displaystyle \frac{3}{2}}& {\displaystyle \frac{1}{2}}\end{array}\right]$

31. $A^{-1}=\left[\begin{array}{rr}5& 3\\ 3& 2\end{array}\right]$

33. $A^{-1}={\displaystyle \frac{1}{b^2-a^2}}\left[\begin{array}{rr}-a& b\\ -b& a\end{array}\right],$ where $a^2\ne b^2$

35. $\left[\begin{array}{rr}2& 3\\ 1& -3\end{array}\right]\left[\begin{array}{l}x\\ y\end{array}\right]=\left[\begin{array}{l}-9\\ 13\end{array}\right]$

37. $\left[\begin{array}{rrr}3& 2& 1\\ 2& 1& 3\\ 1& 3& 2\end{array}\right]\left[\begin{array}{l}x\\ y\\ z\end{array}\right]=\left[\begin{array}{l}8\\ 7\\ 9\end{array}\right]$

39. $\{\begin{array}{rrrrr}x& -& 2y& =& 0\\ 2x& +& y& =& 5\end{array}$

41. $\{\begin{array}{rrrrrrr}2x_1& +& 3x_2& +& x_3& =& -1\\ 5x_1& +& 7x_2& -& x_3& =& 5\\ 4x_1& +& 3x_2& & & =& 5\end{array}$

43. $\left[\begin{array}{rrr}1& 2& 5\\ 2& 3& 8\\ -1& 1& 2\end{array}\right]\left[\begin{array}{rrr}2& -1& -1\\ 12& -7& -2\\ -5& 3& 1\end{array}\right]=\left[\begin{array}{rrr}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$

45. $\{(2,-3,1)\}$

47.

1. $A^{-1}=\left[\begin{array}{rrr}3& -{\displaystyle \frac{5}{2}}& {\displaystyle \frac{1}{2}}\\ -3& 4& -1\\ 1& -{\displaystyle \frac{3}{2}}& {\displaystyle \frac{1}{2}}\end{array}\right]$

2. $\{(1,2,3)\}$