Let $M=\left[ \begin{array} { c c } { - 1 } & { - 5 } \\ { 3 } & { 15 } \end{array} \right]$.  

1. Evaluate $\det(M)$.

   Step (a):

   $(−1)(15) − (3)(−5)$

2. What does your answer to part (a) indicate about $M^{ –1}$?

   Hint (b):

   $A = \left[ \begin{array} { c c } { a } & { b } \\ { c } & { d } \end{array} \right] \text { then } A ^ { - 1 } = \frac { 1 } { \operatorname { det } ( A ) } \left[ \begin{array} { c c } { d } & { - b } \\ { - c } & { a } \end{array} \right]$

3. What does your answer to part (a) indicate about the system at right?

   $\left. \begin{array} { l } { - x - 5 y = 9 } \\ { 3 x + 15 y = 3 } \end{array} \right.$

   Hint (c):

   If you don't know, try solving the system.