Question

If $A$ is a square matrix then $A-A^{\prime }$ is a

• A. diagonal matrix
• B. skew symmetric matrix
• C. symmetric matrix
• D. None of these

Answer 1

The correct option is B skew symmetric matrix

Consider, $(A-A^{\prime }{)}^{\prime }=A^{\prime }-(A^{\prime }{)}^{\prime }$
$=A^{\prime }-A$
$=-(A-A^{\prime })$
$\Rightarrow (A-A^{\prime }{)}^{\prime }=-(A-A^{\prime })$
Hence, $A-A^{\prime }$ is skew-symmetric