Question

Let $A$ and $B$ be two symmetric matrices of same order. Then, the matrix $AB-BA$ is

• A. a symmetric matrix
• B. a skew-symmetric matrix
• C. a null matrix
• D. the identity matrix

Answer 1

Answer: (B)

Given, $A=A^{\prime },B=B^{\prime }$
Now, $(AB-BA{)}^{\prime }=(AB{)}^{\prime }-(BA{)}^{\prime }$
$=B^{\prime }{A}^{\prime }-A^{\prime }{B}^{\prime }$
$=BA-AB$
$=-(AB-BA)$
$\therefore AB-BA$ is a skew-symmetric matrix.