Chapter 3 - Matrices - 3.1 Matrix Operations - Exercises 3.1 - Page 152: 15

$$A^3= \left[\begin{array}{ll}{27} & {0}\\ {-49}&{125}\end{array}\right]$$

Let $$ A=\left[\begin{array}{ll}{3} & {0}\\ {-1}&{5}\end{array}\right], $$ we have $$A^3=AAA=\left[\begin{array}{ll}{3} & {0}\\ {-1}&{5}\end{array}\right]\left[\begin{array}{ll}{3} & {0}\\ {-1}&{5}\end{array}\right]\left[\begin{array}{ll}{3} & {0}\\ {-1}&{5}\end{array}\right]\\ =\left[\begin{array}{ll}{3} & {0}\\ {-1}&{5}\end{array}\right]\left[\begin{array}{ll}{9} & {0}\\ {-8}&{25}\end{array}\right]=\left[\begin{array}{ll}{27} & {0}\\ {-49}&{125}\end{array}\right].$$