Consider a 3 × 3 real symmetric matrix S such that two of its eigen values are a ≠ 0, b ≠ 0 with respective eigen vectors \[\left[ {\begin{array}{*{20}{c}} {{{\text{x}}_1}} \\ {{{\text{x}}_2}} \\ {{{\text{x}}_3}} \end{array}} \right],\left[ {\begin{array}{*{20}{c}} {{{\text{y}}_1}} \\ {{{\text{y}}_2}} \\ {{{\text{y}}_3}} \end{array}} \right].\]   If a ≠ b then x₁y₁ + x₂y₂ + x₃y₃ equals

A. a

B. b

C. ab

Answer: Option D