Question

If A is any square matrix then (1/2) $(A+A^T)$ is a _____ matrix

• A. symmetric
• B. skew symmetric
• C. scalar
• D. identity

Answer 1

The correct option is A symmetric

Given $\frac{1}{2}(A+A^T)$

Let $A+A^T=P$

Then $P^T={(A+A^T)}^T=A+A^T=P$

$\because P^T=P$

$\Rightarrow {(A+A^T)}^T=A+A^T$

$\Rightarrow \frac{1}{2}(A+A^T)$is symmetric

OPTION A