数学试题讲解

设

A = (\begin{array}{ccc} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{array})

为实数域

R

上的

3 \times 3

不可逆方阵. 若

A

的伴随矩阵

A^{*}

为

A^{*} = (\begin{array}{lll} a_{11}^{2} & a_{12}^{2} & a_{13}^{2} \\ a_{21}^{2} & a_{22}^{2} & a_{23}^{2} \\ a_{31}^{2} & a_{32}^{2} & a_{33}^{2} \end{array}),

求

A