$I f A, B$ are symmetric matrices of the same order then $A B - B A$ is

symmetric matrix

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skew symmetric matrix

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Diagonal matrix

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identity matrix

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Solution

The correct option is B skew symmetric matrix
Let $A = [\begin{matrix} a & c c & l \end{matrix}]$
$B = [\begin{matrix} d & f f & e \end{matrix}]$
$A B = [\begin{matrix} (a d + c f) & (a f + c e) (c d + l f) & (c f + l e) \end{matrix}]$
$B A = [\begin{matrix} (d a + f c) & (d c + l f) (f a + c e) & (f c + l e) \end{matrix}]$
$A B - B A = [\begin{matrix} 0 & a f + c e - (d c + l f) - [(a f + c e) - (d c + l f)] & 0 \end{matrix}]$
$∴$ skew symmetric matrix.

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