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

Find the adjoint of the matrix `A=[(-1,-2,-2), (2 ,1,-2), (2,-2, 1)]` and hence show that `A(a d j\ A)=|A|\ I_3` .

Text Solution

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`|A|=|[-1, -2, -2], [2, 1, -2], [2, -2, 1]|=27`
`adj A=[[-3, 6, 6], [-6, 3, -6], [-6, -6, 3]]`
`A.adj A=[[-1, -2, -2], [2, 1, -2], [2, -2, 1]] xx[[-3, 6, 6], [-6, 3, -6], [-6, -6, 3]]=[[27, 0, 0], [0, 27,0], [0, 0, 27]]=27[[1, 0, 0], [0, 1, 0], [0, 0, 1]]`
Hence proved.
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