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If $A$ and $B$ are square matrices of same order and $B$ is a skew symmetric matrix, then $A^{\prime} B A$ is
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Skew symmetric matrix
Given $B$ is skew-symmetric matrix
$\begin{gathered}
\therefore \quad B^{\prime}=-B \\
\left(A^{\prime} B A\right)^{\prime}=A^{\prime} B^{\prime} A=A^{\prime}(-B) A=-\left(A^{\prime} B A\right)
\end{gathered}$
$\therefore A^{\prime} B A$ is skew symmetric matrix.
$\begin{gathered}
\therefore \quad B^{\prime}=-B \\
\left(A^{\prime} B A\right)^{\prime}=A^{\prime} B^{\prime} A=A^{\prime}(-B) A=-\left(A^{\prime} B A\right)
\end{gathered}$
$\therefore A^{\prime} B A$ is skew symmetric matrix.
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