1. Tardigrade
  2. Question
  3. Mathematics
  4. If A and B are symmetric matrices of the same order, then

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. If A and B are symmetric matrices of the same order, then

Matrices

Solution:

$\left(AB + BA\right)^{t} = \left(AB\right)^{t} + \left(BA\right)^{t} $
$ = B^{t} A^{t} + A^{t} B^{t} =BA + AB = AB + BA $
$ \left(\because A^{t} =A \, \text{and} \, B^{t} =B\right) $