Fundamental theorem of Orthogonality

[Hymne]

Hello there!

I have a group represented by the following matricies:

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

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