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

Let A be a square matrix such that each element of a row/column of A is expressed as the sum of two or more terms. Then, the determinant of A can be expressed as the sum of the determinants of two or more matrices of the same order.

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Knowledge Check

  • If A and B are any two square matrices of the same order than ,

    A
    `(AB)'=A'B'`
    B
    adj ( AB) = adj( A) adj (B)
    C
    (AB) '=B'A'
    D
    AB = O `rArr ` A = O or B =O

  • If each element in a row of a determinant is multiplied by the same factor r, then the value of the determinant

    A
    A. Is multiplied by `r^(3)`
    B
    B. Is increased by 3r
    C
    C. Remains unchanged
    D
    D. Is multiplied by r

  • Let A be a square matrix of order 3 so that sum of elements of each row is 1 . Then the sum elements of matrix A^(2) is

    A
    `1`
    B
    `3`
    C
    `0`
    D
    `6`

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    If any two rows (or columns) of a determinant are identical, the value of the determinant is zero.

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