The positive value of 'a' for which the system of linear homogeneous equations $x+a y+z=0, a x+2 y-z=0,2 x+3 y+z=0$ has non-trivial solutions is

• A

  $0$
• B

  $1$
• Correct answer
  C

  $\frac{1+\sqrt{5}}{2}$
• D

  $\frac{\sqrt{5}-1}{2}$

Hence, the correct answer is option: 'C'.