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Let A be a square matrix such that A^...

Let `A` be a square matrix such that `A^2-A+I=O` , then write `A^(-1)` in terms of `Adot`

Text Solution

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`A^2−A+I=0=A−A^2=I`
or `A(I−A)=I`
` A^(−1)=I−A`
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Knowledge Check

  • If A is a square matrix such that A A^T=I=A^TA , then A is

    A
    a symmetric matrix
    B
    a skew-symmetric matrix
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  • If A is a square matrix such that A^(2)=A, then (I-A)^(2)+A=

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    D
    `I-A`

  • If A is square matrix such that |A| ne 0 and A^2-A+2I=O " then " A^(-1) =?

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

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