If $\left|\begin{array}{ccc}{\alpha }^{2n}& {\alpha }^{2n+2}& {\alpha }^{2n+4}\\ {\beta }^{2n}& {\beta }^{2n+2}& {\beta }^{2n+4}\\ {\gamma }^{2n}& {\gamma }^{2n+2}& {\gamma }^{2n+4}\end{array}\right|=\left(\frac{1}{{\beta }^2}-\frac{1}{{\alpha }^2}\right)\left(\frac{1}{{\gamma }^2}-\frac{1}{{\beta }^2}\right)\left(\frac{1}{{\alpha }^2}-\frac{1}{{\gamma }^2}\right)$ {where ${\alpha }^2, {\beta }^2$ and ${\gamma }^2$ are all distinct}, then the value of $n$ is equal to

• A

  $4$
• B

  $-4$
• C

  $3$
• Correct answer
  D

  $-2$

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