Using Trace to Determine Orthogonality of Matrices

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Is there a way to use the trace of a matrix to find whether a set of matrices are orthogoal to one another?
 
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Is the trace the only thing known ?
You just have trace = x ?
 
Since tr(AB) = tr(BA) (sorry wrong terminology), so just apply the definition of an orthogonal matrix.
 
konthelion said:
Since tr(AB) = tr(BA) (sorry wrong terminology), so just apply the definition of an orthogonal matrix.

can you explain this further?
 

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