The characteristic equation can be rewritten as :
λ^{3} + 2 λ^{2} + 2 λ + 1 = 0
==> λ ( λ^{2} + 2 λ + 1) + 1(λ + 1) = 0
==> λ (λ + 1)^{2} + 1(λ + 1) = 0
==> (λ + 1) (λ^{2 }+ λ + 1) = 0
Solving which we get λ = -1 , ω , ω^{2} ^{ }where ω , ω^{2 }are cube roots of unity ..
As we know :
Modulus of each of cube roots of unity = | ω | = | ω^{2 }| = 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..