Question

If A and B are symmetric matrices of same order then
A. AB is symmetric iff $AB=BA$

B. $AB+BA$ is skew symmetric matrix

C. AB-BA is symmetric matrix

D. $(A+B)^{n}$ is symmetric for all $n \in N$

Choose the correct answer from the options given below

• A. A, B only
• B. B, C only
• C. C, D only
• D. A, D only

Hint:

Always remember the property $(AB)^T = B^T A^T$. If two symmetric matrices commute ($AB=BA$), their product remains symmetric. If they do not, their product is generally neither symmetric nor skew-symmetric.

Answer 1

The Correct Option is D