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\title{General Mathematics and CPS II}
\author{Exercise 7}
\date{February 24, 2012}
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\begin{enumerate}

\item Use the matrix form of the equation for a reflection (see
handout) to show that the composition of reflections about parallel
lines is a translation $\Pi_{\boldsymbol v}$.  Find an expression for the
translation vector $\boldsymbol v$.

\item Let $G$ be a group and let $a,b \in G$.  Show that
$(ab)^{-1}=b^{-1} \, a^{-1}$.

\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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