已知向量组（ I ） $\boldsymbol{\alpha}_1=\left(\begin{array}{l}1 \\ 0 \\ 1 \\ 0\end{array}\right), \boldsymbol{\alpha}_2=\left(\begin{array}{l}0 \\ 2 \\ 0 \\ 0\end{array}\right), \boldsymbol{\alpha}_3=\left(\begin{array}{l}0 \\ 0 \\ 3 \\ 0\end{array}\right)$ ，（II） $\boldsymbol{\beta}_1=\left(\begin{array}{l}0 \\ 0 \\ 0 \\ 4\end{array}\right), \boldsymbol{\beta}_2=\left(\begin{array}{l}0 \\ 0 \\ 5 \\ 0\end{array}\right), \boldsymbol{\beta}_3=\left(\begin{array}{l}6 \\ 6 \\ 0 \\ 0\end{array}\right)$ 和矩阵 $\boldsymbol{A}= \left(\boldsymbol{\alpha}_1, \boldsymbol{\alpha}_2, \boldsymbol{\alpha}_3\right), \boldsymbol{B}=\left(\boldsymbol{\beta}_1, \boldsymbol{\beta}_2, \boldsymbol{\beta}_3\right)$ ，则