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Find A^(-1) if A=|(0,1,1),(1,0,1),(1,1,0...

Find `A^(-1)` if `A=|(0,1,1),(1,0,1),(1,1,0)|` and show that `A^(-1)=(A^(2)-3I)/2`

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`A=|(0,1,1),(1,0,1),(1,1,0)|`
`adj A=A=|(0,1,1),(1,0,1),(1,1,0)|^7=[[-1, 1, 1], [1, -1, 1], [1, 1, -1]]` and `|A|=-1(-1)+1.1=2`
`A^(-1)=frac{adj A}{|A|}`
`=1/2 [[-1, 1, 1], [1, -1, 1], [1, 1, -1]]`----(i)
`A^2=[[0, 1, 1], [1, 0, 1], [1, 1, 0]] [[0, 1, 1], [1, 0, 1], [1, 1, 0]]=[[2, 1, 1],[1, 2, 1], [1, 1, 2]]`----(ii)
`frac{A^2-3I}{2}=1/2 {[[2, 1, 1], [1, 2, 1], [1, 1, 2]]-[[3, 0, 0], [0, 3, 0], [0, 0, 3]]}=1/2 |[-1, 1, 1], [1, -1, 1], [1, 1, -1]|=A^(-1)`
Hence, proved.
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