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If A = [[1,-2,3],[0,-1,4],[-2,2,1]] ,find (A')-1 - Mathematics

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If A = `[[1,-2,3],[0,-1,4],[-2,2,1]]` ,find (A')-1

 
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Solution

`A=[[1,-2,3],[0,-1,4],[-2,2,1]]`

`=>A'=[[1,0,-2],[-2,-1,2],[3,4,1]]`

Now 

`|A'|=|[1,0,-2],[-2,-1,2],[3,4,1]|=1(-1-8)-0(-2-6)-2(-8+3)=-9+10=1ne 0`

`adjA'=[[-9,-8,-2],[8,7,2],[-5,-4,-1]]`

`therefore (A')^-1="adjA'"/|A'|`

`=>(A')^-1=[[-9,-8,-2],[8,7,2],[-5,-4,-1]]`

 

Concept: Inverse of Matrix - Inverse of a Nonsingular Matrix by Elementary Transformation
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