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Compute the inverse of the matix A = [{:...

Compute the inverse of the matix `A = [{:(0,1,2),(1,2,3),(0,1,2):}]`

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We have,`A = [{:(0,1,2),(1,2,3),(0,1,2):}]`
Then," " ` A = [{:(0,1,2),(1,2,3),(0,1,2):}] = 0.(2-3)-1(1-9)+2(1-6)`
`=-2!=0`
`therefore A^(-1)` exists.
Now, cofactors along `R_(1)=-1,8,-5`
cofactors along ` R_(2)=1,-6,3`
cofactors along `R_(3)=-1,2,-1`
Let C is a matrix of cofactors of the elements in `|A|`
`therefore C=[(-1,8,-5),(1,-6,3),(-1,2,-1)]`
`therefore" ""adj" A= C'=[(-1,1,-1),(8,-6,2),(-5,3,-1)]`
Hence, `A^(-1)=(adjA)/|A|=-(1)/(2)[(-1,1,-1),(8,-6,2),(-5,3,-1)]`
`=[((1)/(2),-(1)/(2),(1)/(2)),(-4,3,-1),((5)/(2),-(3)/(2),(1)/(2))]`
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