Question

If $A$ and $B$ are symmetric matrices of order $n,(A\ne B)$, then

• A. $A+B$ is skew-symmetric
• B. $A+B$ is symmetric
• C. $A+B$ is a diagonal matrix
• D. $A+B$ is a zero matrix

Answer 1

Answer: (B)

$A+B$ is symmetric

Since $A$ and $B$ are symmetric matrices, $A^{\prime }=A$ and $B^{\prime }=B$

$\therefore (A+B{)}^{\prime }=A^{\prime }+B^{\prime }=A+B$

$\therefore A+B$ is symmetric matrix