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

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

Text Solution

Verified by Experts

The correct Answer is:
B
Given A'=A and B'=B
`therefore(AB-BA)'=(AB)'-(BA)'=(B'A'-A'B')=(BA-AB)=-(AB-BA)`
`therefore(AB-BA)` is skew symmetric
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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 symmetric matrices of the same order then AB-BA is a matrix which is

    A
    null
    B
    unit
    C
    symmetric
    D
    skew symmetric

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