Chapter 3 - Determinants - 3.2 Determinants and Elementary Operations - 3.2 Exercises - Page 118: 22

$$\left|\begin{array}{rrr}{-1} & {3} & {2} \\ {0} & {2} & {0} \\ {1} & {1} & {-1}\end{array}\right|=-2.$$

\begin{align*} \left|\begin{array}{rrr}{-1} & {3} & {2} \\ {0} & {2} & {0} \\ {1} & {1} & {-1}\end{array}\right|&=-0\left|\begin{array}{rrr} {3} & {2} \\ {1} & {-1}\end{array}\right|+2 \left|\begin{array}{rrr} {-1} & {2} \\ {1} & {-1}\end{array}\right|-0\left|\begin{array}{rrr} {-1} & {3} \\ {1} & {1}\end{array}\right|\\ &=2(-1)\\ &=-2. \end{align*}