设三阶矩阵 $\boldsymbol{A}$ 满足: $\boldsymbol{A} \boldsymbol{X}_1=\boldsymbol{X}_1, \boldsymbol{A} \boldsymbol{X}_2=\mathbf{0}, \boldsymbol{A} \boldsymbol{X}_3=-\boldsymbol{X}_3$, 其中 $\boldsymbol{X}_1=(1,1,0)^{\mathrm{T}}, \boldsymbol{X}_2=(0,1,0)^{\mathrm{T}}, \boldsymbol{X}_3=(0,0,1)^{\mathrm{T}}$,求(1) $\left|\boldsymbol{A}^2-\boldsymbol{A}+3 \boldsymbol{E}\right|$;
(2)矩阵 $\boldsymbol{A}, \boldsymbol{A}^{10}$.