Could you please elucidate further? Thank you in advance.

9 votes

Best answer

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.. **