Let m be a positive real number and $u = \left[ \begin{array} { l l } x & y \end{array} \right]$. Given that
$$\mathrm { u } \cdot \left[ \begin{array} { l l }
1 & 2 \\
2 & 1
\end{array} \right] = \mathrm { u } \cdot \left[ \begin{array} { c c }
\mathrm { m } & 0 \\
0 & \mathrm {~m}
\end{array} \right]$$
the matrix equation has infinitely many solutions for u, what is m?\\
A) $\frac { 1 } { 2 }$\\
B) $\frac { 1 } { 3 }$\\
C) $\frac { 2 } { 3 }$\\
D) 3\\
E) 4