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Find the matrix A such that |A|=2 and ad...

Find the matrix A such that `|A|=2` and `adj(A)=[[2,2, 0],[ 2, 5, 1],[ 0, 1, 1]]`

Text Solution

Verified by Experts

Given,
`adjA=[(2, 2, 0),( 2, 5, 1),( 0, 1 ,1)]`

`|A|=2`

We know

`A*adjA=|A|I=adj(A)*A`

`implies A=|A|I(adjA)^(-1)`

`implies A=2(B)^(-1)`

`B^(-1)=1/|B|adj(B)`

`|B|=|adj(A)|=2(5-1)-2(2-0)+0=4`

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