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If A is a square matrix such that |A| ne...

If A is a square matrix such that `|A| ne 0 and m, n (ne 0)` are scalars such that `A^(2)+mA+nI=0`, then `A^(-1)=`

A

`-(1)/(m)(A+nI)`

B

`-(1)/(n)(A+mI)`

C

`-(1)/(n)(I+mA)`

D

`(1)/(n)(I+mA)`

Text Solution

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The correct Answer is:
b
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Knowledge Check

  • If A^(2)+mA+nI=O&n ne0,|A|ne0 , then A^(-1) =………..

    A
    `(-1)/(m)(A+nI)`
    B
    `(-1)/(n)(A+mI)`
    C
    `(-1)/(n)(A+mA)`
    D
    `(A+mnI)`

  • If A is a 2xx2 matrix such that A(adj.A)=[(5,0),(0,5)] , then |A|= ……..

    A
    0
    B
    5
    C
    10
    D
    25

  • If x sqrt(y+1)+ y sqrt(x+1)= 0 and x ne y " then " (dy)/(dx) = ….

    A
    `(1)/((1+ x)^(2))`
    B
    `-(1)/((1+ x)^(2))`
    C
    `(1+ x)^(2)`
    D
    `-(x)/(x+1)`

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