Given that A and B are n times n symmetric matrices Prove th

Given that A and B are n times n symmetric matrices, Prove that A + B is also symmetric.

Solution

Solution:

A square matrix A is said to be symetric if A^T= A

Here A and B is symetric.Therefore A^T=A and B^T=B.

Now (A+B)^T=A^T+B^T= A+B

Thus, (A+B)T= A+B. Hence A+B is symetric.