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\title{General Mathematics and ACM II}
\author{Exercise 6}
\date{February 23, 2011}
\maketitle

\begin{enumerate}

\item (Ivanov, p.\ 36, Problem~14.)  Show that
  \begin{enumerate}
  \item $R_{\ell_1} \, R_{\ell_2} = R_{\ell_2} \, R_{\ell_1}$ if and
  only if $\ell_1$ and $\ell_2$ are perpendicular;
  \item  $R_{\ell} \, H_A = H_A \, R_{\ell}$ if and
  only if $A \in \ell$.
  \end{enumerate}


\item (Ivanov, p.\ 39.)  Recall that the symmetry group of a subset
$A$ of the plane is defined as
\[
  \operatorname{Sym}(A) = \{ F \text{ motion} \colon F(A)=A \} \,.
\]
Prove that such a set of motions is indeed a group. 

\end{enumerate}
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