Question

If $A$ is a square matrix. $A^{\prime }$ its transpose, then $\frac{1}{2}(A-A^{\prime })$ is

• A. a symmetric matrix
• B. a skew symmetric matrix
• C. a unit matrix
• D. an elementary matrix

Answer 1

Answer: (B)

Now, ${\left[\frac{1}{2}(A-A^{\prime })\right]}^{{}^{\prime }}=\frac{1}{2}(A-A^{\prime }{)}^{\prime }$
$=\frac{1}{2}(A^{\prime }-A)$
$=-\frac{1}{2}(A-A^{\prime })$
Hence, it is a skew symmetric matrix.