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If In is the identity matrix of order n ...

If `I_n` is the identity matrix of order n then `(I_n)^-1` (A) does not exist (B) `=0` (C) `=I_n` (D) `=nI_n`

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If I_3 is the identity matrix of order 3 then I_3^-1 is (A) 0 (B) 3I_3 (C) I_3 (D) does not exist

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Knowledge Check

  • If I is unit matrix of order n, then 3I will be

    A
    a unit matrix
    B
    a scalar matrix
    C
    a triangular matrix
    D
    a zero matrix

  • Let A be an orthogonal non-singular matrix of order n, then |A-I_n| is equal to :

    A
    `|I_n-A|`
    B
    `|A|`
    C
    `|A||I_n-A|`
    D
    `(-1)^n |A||I_n-A|`

  • If B_(0)=[(-4, -3, -3),(1,0,1),(4,4,3)], B_(n)=adj(B_(n-1), AA n in N and I is an identity matrix of order 3, then B_(1)+B_(3)+B_(5)+B_(7)+B_(9) is equal to

    A
    `B_(0)`
    B
    `5B_(0)`
    C
    `25B_(0)`
    D
    `5I`

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    A square matrix M of order 3 satisfies M^(2)=I-M , where I is an identity matrix of order 3. If M^(n)=5I-8M , then n is equal to _______.

    Which of the following statements is/are true about square matrix A or order n?(-A)^(-1) is equal to -A^(-1) when n is odd only If A^(n)-O, then I+A+A^(2)+...+A^(n-1)=(I-A)^(-1) If A is skew-symmetric matrix of odd order,then its inverse does not exist.(A^(T))^(-1)=(A^(-1))^(T) holds always.

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