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  4. If A and B are square matrices of same order and B is a skew symmetric matrix, then A'BA is

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Q. If $A$ and $B$ are square matrices of same order and $B$ is a skew symmetric matrix, then $A'BA$ is

KCETKCET 2020Matrices

Solution:

$B$ is a skew symmetric matrix.
$\Rightarrow B'=- B$
Now, $\left(A' B A\right)'=A' B'\left(A'\right)'$
$=A'(-B) A$
$=-\left(A'B A\right)$
Hence, $A'BA$ is a skew symmetric matrix.