Chapter 14.7, Problem 11WE

To determine

To give : the image of $A$ under rotation of $R^{-3}\cdot R^3$ .

Explanation of Solution

Given information : The rotation $R$ maps all points ${90}^{\circ }$ about $O$ , the centre of square $ABCD$ .

From the above figure it is observed that:

  $\begin{array}{l}{R}^{-3}\cdot R^3\\ \Rightarrow R^{-3}\cdot \left(R^3\left(A\right)\right)\\ \Rightarrow R^{-3}\cdot \left(D\right)\\ \Rightarrow A\end{array}$