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A ,\ B are two matrices such that A B...

`A ,\ B` are two matrices such that `A B` and `A+B` are both defined; show that `A ,\ B` are square matrices of the same order.

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If A and B are two matrices such that A + B and AB are both defined, then

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Knowledge Check

  • If A and B are square matrices of same order, then

    A
    `A-B=B-A`
    B
    A+B=B-A
    C
    `A+B=B+A`
    D
    `AB=BA`

  • 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 A and B are square matrices of order 3, then

    A
    ` adj (AB) =adjA + adj B `
    B
    `(A+B) =A^(-1) +B^(-1) `
    C
    ` AB= O rArr | A| =0 or [B] =0`
    D
    ` AB = OrArr |A| =0 and |B| =0`

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