Fundamental theorem of Orthogonality

[Hymne]

Hello there!

I have a group represented by the following matricies:


\left( \begin{array}{cc}
1 & 0 \\
0 & 1 \end{array} \right)\] ; 0.5\left( \begin{array}{cc}
-1 & \sqrt{3} \\
-\sqrt{3} & -1 \end{array} \right)\] and\quad 0.5
\left( \begin{array}{cc}
-1 & -\sqrt{3} \\
\sqrt{3} & -1 \end{array} \right)\]



These does not however, seem to fulfill the F O T, what does this mean? It seems to be a irreducible representation :/

[homology]

(1) Is this homework?
(2) What does the fundamental theorem of orthogonality state?

[fzero]

Those matrices are not linearly independent:

0.5\left( \begin{array}{cc}
-1 & \sqrt{3} \\
-\sqrt{3} & -1 \end{array} \right)\] = - 0.5 \left( \begin{array}{cc}
-1 & -\sqrt{3} \\
\sqrt{3} & -1 \end{array} \right)\] - 2I.