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If A is a non-singular matrix, prove th...

If A is a non-singular matrix, prove that: `adjA` is also non -singular `(adjA)^-1=1/|A| A`.

Text Solution

Verified by Experts

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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Knowledge Check

  • If A is a non-singular matrix, then

    A
    `A^(-1)` is a non-singular matrix, then
    B
    `A^(-1)`is skew-symmetric if A is symmetric
    C
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    D
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    identity matrix
    B
    null matrix
    C
    scalar matrix
    D
    diagonal matrix

  • If A and B are non-singular matrices, then

    A
    `AB=BA`
    B
    `(AB)'=A'B'`
    C
    `(AB)^(-1)=B^(-1)A^(-1)`
    D
    `(AB)^(-1)=A^(-1)B^(-1)`

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