Consider the matrix $A=\left[\begin{array}{ccc}x& 2y& z\\ 2y& z& x\\ z& x& 2y\end{array}\right]$ and $A{A}^T=9I$. If $Tr\left(A\right)>0$ and $xyz=\frac{1}{6}$, then the value of $x^3+8y^3+z^3$ is equal to (where, $Tr\left(A\right), I$ and $A^T$ denote the trace of matrix $A$ i.e. the sum of all the principal diagonal elements, the identity matrix of the same order of matrix $A$ and the transpose of matrix $A$ respectively)

• A

  $20$
• B

  $22$
• C

  $26$
• Correct answer
  D

  $28$

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