### Home > PC3 > Chapter 9 > Lesson 9.2.2 > Problem9-118

9-118.

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

1. Evaluate $\det(M)$.

$(−1)(15) − (3)(−5)$

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

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

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