Chapter 14.7, Problem 17WE

To determine

  $H_0{}^3$ is the same as the mapping _______.

Answer to Problem 17WE

  $H_0{}^3$ is the same as the mapping $H_0$ .

Explanation of Solution

  $\begin{array}{l}{H}_0{}^3\\ =\left(H_0{}^2\right)\left(H_0\right)\\ =I\circ H_0\\ =H_0\end{array}$

Hence,

  $H_0{}^3$ is the same as the mapping is $H_0$ .