Let A= [2, 0, 1; 1, 1, 0; 1, 0, 1], B=[B_1, B_2, B_3], where B_1, B_2, B_3 are column matrics, and A B_1= [1; 0; 0], A B_2= [2; 3; 0], A B_3= [3; 2;…

Let $\displaystyle A=\left[\begin{array}{lll}2 & 0 & 1 \\ 1 & 1 & 0 \\ 1 & 0 & 1\end{array}\right], B=\left[B_1, B_2, B_3\right]$, where $\displaystyle B_1, B_2, B_3$ are column matrics, and $$A B_1=\left[\begin{array}{l} 1 \\ 0 \\ 0 \end{array}\right], A B_2=\left[\begin{array}{l} 2 \\ 3 \\ 0 \end{array}\right], A B_3=\left[\begin{array}{l} 3 \\ 2 \\ 1 \end{array}\right] $$ If $\displaystyle \alpha=|\mathrm{B}|$ and $\displaystyle \beta$ is the sum of all the diagonal elements of B , then $\displaystyle \alpha^3+\beta^3$ is equal to $\displaystyle \_\_\_\_$.