Question

If A and B are symmetric matrices of the same order, prove that AB+BA is symmetric.
Hint:Prove that (AB+BA)'=AB+BA.​

Answer 1

Step-by-step explanation:

A'=A and B'=B

(AB+BA)'

(AB)'+(BA)'

B'A' + A'B'

BA + AB or AB+BA

(AB+BA)'=(AB+BA)

therefore, (AB+BA) is symmetric matric.