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Let A =[(1,-1,1),(2,1,-3),(1,1,1)] an...

Let `A =[(1,-1,1),(2,1,-3),(1,1,1)]` and `10B=[(4,2,2),(-5,0,alpha),(1,-2,3)]`. If B is the inverse of A, then find the value of `alpha`

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Here,
`A=[(1,-1,1),(2,1,-3),(1,1,1)]`
`:. |A|=|(1,-1,1),(2,1,-3),(1,1,1)|`
`=1(1+3)+1(2+3)+1(2-1)`
`=4+5+1=10`
Now, adj `A=[(4,-5,1),(2,0,-2),(2,5,3)]^(T)=[(4,2,2),(-5,0,5),(1,-2,3)]`
`implies B=A^(-1) =1/10 [(4,2,2),(-5,0,5),(1,-2,3)]`
`implies 10 B =[(4,2,2),(-5,0,5),(1,-2,3)]`
Hence, `alpha=5`.
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