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The characteristic equation of matrix A is $$\lambda ^3 - I_1\lambda^2 + I_2\lambda-I_3 = 0 $$

For orthogonal matrix $$I_3 = det(A) = \pm1$$ $$I_1 = tr(A)$$

Taking examples of orthogonal matrices, it looks like $I_1 = I_2$. Is this true always for an orthogonal matrix? Is there some proof?

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