7.

$$A = \left( \begin{array} { c c } 
- \frac { \sqrt { 3 } } { 2 } & - \frac { 1 } { 2 } \\
\frac { 1 } { 2 } & - \frac { \sqrt { 3 } } { 2 }
\end{array} \right)$$
\begin{enumerate}[label=(\alph*)]
\item Determine the matrix $\mathbf { A } ^ { 2 }$
\item Describe fully the single geometrical transformation represented by the matrix $\mathbf { A } ^ { 2 }$
\item Hence determine the smallest positive integer value of $n$ for which $\mathbf { A } ^ { n } = \mathbf { I }$

The matrix $\mathbf { B }$ represents a stretch scale factor 4 parallel to the $x$-axis.
\item Write down the matrix $\mathbf { B }$

The transformation represented by matrix $\mathbf { A }$ followed by the transformation represented by matrix $\mathbf { B }$ is represented by the matrix $\mathbf { C }$
\item Determine the matrix $\mathbf { C }$

The parallelogram $P$ is transformed onto the parallelogram $P ^ { \prime }$ by the matrix $\mathbf { C }$
\item Given that the area of parallelogram $P ^ { \prime }$ is 20 square units, determine the area of parallelogram $P$
\end{enumerate}

\hfill \mbox{\textit{Edexcel F1 2022 Q7 [9]}}