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The characteristic equation can be rewritten as :

λ3  +  2 λ2  + 2 λ + 1  =  0

==>   λ ( λ2  +  2 λ + 1)  + 1(λ + 1)  =  0

==>    λ (λ + 1)2  + 1(λ + 1)  =  0

==>    (λ + 1) (λ+ λ + 1)   =  0

Solving which we get λ = -1 , ω  , ω2  where ω  , ωare cube roots of unity ..

As we know :

Modulus of each of cube roots of unity  =  | ω |  =  | ω|  =  1

Also we know ,

Eigen values of matrix satisfies the corresponding characteristic equation and if all eigen values have modulus value = 1 , then the matrix is said to be orthogonal.

which is the case here..

Hence C) is the correct answer..

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