# Are the invariants related in the characteristic equation of an orthogonal matrix (3x3 matrix)?

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?