Question

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

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

Answer 1

Answer: (B)

a skew symmetric matrix

Answer 2

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