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Let A = (a(ij))(1 le I, j le 3) be a 3 x...

Let `A = (a_(ij))_(1 le I, j le 3)` be a `3 xx 3` invertible matrix where each `a_(ij)` is a real number. Denote the inverse of the matrix A by `A^(-1)`. If `Sigma_(j=1)^(3) a_(ij) = 1` for `1 le i le 3`, then

A

sum of the diagonal entries of A is 1

B

sum of each row of `A^(-1)` is 1

C

sum of each row and each column of `A^(-1)` is 1

D

sum of the diagonal entries is `A^(-1)` is 1

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Knowledge Check

  • Let A= (a_(ij))_(1 le I , j le 3) be a 3 xx 3 invertible matrix where each a_(ij) is a real number. Denote the inverse of the matrix A by A^(–1) . If sum_(j=1)^(3) a_(Ij) = 1 for 1 le i le 3 , then

    A
    sum of the diagonal entries of A is 1
    B
    sum of each row of `A^(–1)` is 1
    C
    sum of each row and each column of `A^(–)`1 is 1
    D
    sum of the diagonal entries of `A^(–1)` is 1

  • A is a matrix of 3xx3 and a_(ij) is its elements of i^(th) row and j^(th) column. If a_(ij)+a_(jk)+a_(ki)=0 holds for all 1 le i, j, kle 3 then

    A
    `A` is a non singular matrix
    B
    `A` is a singular matrix
    C
    `sum_(1 let i, j le 3)a_(ij)` is equal to zero
    D
    `A` is a symmetric matrix

  • Let A = [{:(1,2),(3,4):}]=[a_(ij)] , where i, j = 1, 2, If its inverse matrix is [b_(ij)] , what is b_(22) ?

    A
    -2
    B
    1
    C
    `(3)/(2)`
    D
    `-(1)/(2)`

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