If A and B be symmetric matrices of the same order, then AB-BA will be

Symmetric matrix

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Skew symmetric matrix

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Null matrix

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None of these

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Solution

The correct option is B
Skew symmetric matrix

Since, A and B are symmetric $\Rightarrow$ A = A' and B = B'

$∴$ (AB-BA)' = (AB)' - (BA)' = B'A' - A'B'

= - (A'B'-B'A') = - (AB-BA)

$\Rightarrow$ (AB-BA) is skew-symmetric.

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Choose the correct answer in the following question:

If A,B are symmetric matrices of same order, then AB-BA is a
(a)skew-symmetric matrix
(b)symmetric matrix
(c)zero matrix
(d)identity matrix

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If A and B be symmetric matrices of the same order, then AB-BA will be

The correct option is B Skew symmetric matrix Since, A and B are symmetric ⇒ A = A' and B = B' ∴ (AB-BA)' = (AB)' - (BA)' = B'A' - A'B' = - (A'B'-B'A') = - (AB-BA) ⇒ (AB-BA) is skew-symmetric.

The correct option is B
Skew symmetric matrix

Since, A and B are symmetric $\Rightarrow$ A = A' and B = B'

$∴$ (AB-BA)' = (AB)' - (BA)' = B'A' - A'B'

= - (A'B'-B'A') = - (AB-BA)

$\Rightarrow$ (AB-BA) is skew-symmetric.