If A is a non-singular matrix, prove that: `adjA` is also non -singular `(adjA)^-1=1/|A| A`.
Text Solution
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Let,
`(adj(A))^-1 = B`
We know that, `A A^-1 =I`
Multiply `adj(A)` both sides
`(adjA)^-1 adj(A)=1/|A| A adj(A)`
`I=1/|A| A adj(A)`
`LHS =I`
We know that, `Aadj(A) = I |A|`
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