Given matrix M and vector X where:

$\displaystyle

\[M =

\left( {\begin{array}{cc}

cos\theta & sin\theta \\

-sin\theta & cos\theta

\end{array} } \right) \]

\textit{and}

X =

\left( {\begin{array}{cc}

x \\

y

\end{array} } \right)

$

Compute: $\displaystyle

\frac { \left|{MX}\right|}{\left|{X}\right|}

$

So I found that the result is 1.

The question is to explain the result and describe the action of M geometrically.

I think the result means that

$\displaystyle

\[M =

\left( {\begin{array}{cc}

1 & 0 \\

0 & 1

\end{array} } \right) \]

$

which, geometrically, doesn't change the length of vector X. Would that be correct?