Chapter 14.7, Problem 28WE

To determine

To find a transformation S (other than the activity) for which $S^5=I$

Answer to Problem 28WE

The Transformation S is equal to the inverse of T

Explanation of Solution

Given information :

  $S^5=I$

Let’s say,

  $S\circ T=I$

Taking 5^th power on both sides

  $\begin{array}{l}{\left(S\circ T\right)}^5=I^5\\ S^5\circ T^5=I\end{array}$

  $S^5=I$ (Given)

  $\begin{array}{l}I\circ T^5=I\\ T^{-5}=I\\ $ {(T^{-1})}^5=I$T^{-1}=I\end{array}$

Hence,

Hence, Transformation S is equal to the inverse of T