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Find the adjoint of the matrix A=[(1,1,1...

Find the adjoint of the matrix `A=[(1,1,1),(2,1,-3),(-1,2,3)]`.

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Let `C_("ij")` be a cofactor of `a_("ij")` in A. Then, the cofactors elements of A are given by
`C_(11)=|(1,-3),(2,3)|=9`
`C_(12)=-|(2,-3),(-1,3)|=-3`
`C_(13)=|(2,1),(-1,2)|=5`
`C_(21)=-|(1,1),(2,3)|=-1`
`C_(22)=|(1,1),(-1,3)|=4`
`C_(23)=-|(1,1),(-1,2)|=-3`
`C_(31)=|(1,1),(1,-3)|=-4`
`C_(32)=-|(1,1),(2,-3)|=5`
`C_(33)=|(1,1),(2,1)|=-1`
`:.` adj `A=[(9,-3,5),(-1,4,-3),(-4,5,-1)]^(T)=[(9,-1,-4),(-3,4,5),(5,-3,-1)]`
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