8.已知alpha=(1,2,3),beta=(1,(1)/(2),(1)/(3)),矩阵A=alpha^Tbeta,其中alpha^T是alpha的转置，求A^n(n为正整数)。

8.已知$\alpha=(1,2,3)$,$\beta=(1,\frac{1}{2},\frac{1}{3})$,矩阵$A=\alpha^{T}\beta$,其中$\alpha^{T}$是$\alpha$的转置，求$A^{n}$(n为正整数)。

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