If the matrix $A=\left[\begin{array}{cc}\alpha & 0\\ 2& \alpha \end{array}\right]$ $\left(\forall \alpha \in R, \alpha >0\right)$ and $\left|2A^2-2A\right|=144,$ then the value of $\left|A\right|+tr\left(A\right)$ is equal to (where $t_r\left(A\right)$ represent the trace of the matrix $A$ i.e. the sum of all the principal diagonal elements  of the matrix $A$ and $\left|A\right|$ is the determinant value of $A$) 

• A

  $8$
• Correct answer
  B

  $15$
• C

  $20$
• D

  $24$

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