Compute the adjoint of
the matrix `A`
given by ,`A=[[1,-2,-2],[2,1,−2],[2,−2,1]]`
and verify that `A(adjA)=|A|I=(adj A)Adot`
Text Solution
Verified by Experts
Given,`A=[[1,-2,-2],[2,1,−2],[2,−2,1]]`
`|A|=[[1,-2,-2],[2,1,−2],[2,−2,1]]`=27
Now,Adjoint of a matrix is the transpose of its' cofactor matrix.
`adj(A)=[[−3,−6,6],[-6,3,−6],[-6,−63]]`
`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]]`
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