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  4. If a matrix A is symmetric as well as skew symmetric, then

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Q. If a matrix A is symmetric as well as skew symmetric, then

Matrices

Solution:

Since A is symmetric $\therefore $ A' = A
Since A is skew symmetric $\therefore $ A' = - A .
$\therefore $ A = - A $\Rightarrow $ 2A = O $\Rightarrow $ A = O.