Question

If $A$ and $B$ are square matrices of same order and $B$ is a skew symmetric matrix, then $A^{\prime }BA$ is

• A. Symmetric matrix
• B. Null matrix
• C. Diagonal matrix
• D. Skew symmetric matrix

Answer 1

Answer: (D)

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