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If A and B are symmetric matrices of sam...

If A and B are symmetric matrices of same order, then AB is symmetric if and only if.......

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If A and B are symmetric matrices of same order, then Ab is symmetric if and only is AB=BA.
`therefore (AB)'`
=B'A'=BA
=AB `[because AB=BA]`
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Knowledge Check

  • If A,B are symmetric matrices of same order, them AB-BA is a :

    A
    Skew - symmetric matrix
    B
    Symmetric matrix
    C
    Zero matrix
    D
    Identity matrix.

  • If A and B are matrices of same order, then (AB'-BA') is a

    A
    skew-symmetric matrix
    B
    unit matrix
    C
    symmetric matrix
    D
    unit matrix

  • If A and B are symmetric matrices of the same order then (AB-BA) is always

    A
    a symmetric matrix
    B
    a skew symmetric matrix
    C
    a zero matrix
    D
    an identity matrix

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