Get Answers to all your Questions

header-bg qa

Q4.    If A and B are symmetric matrices, prove that AB - BA is a skew symmetric matrix.

Answers (1)

best_answer

  If A, B are symmetric matrices then 

                                                 A'=A       and      B' = B

we have,             \left ( AB-BA \right )'=\left ( AB \right )'-\left ( BA \right )'=B'A'-A'B'

                                                                                             =BA-AB

                                                                                             = -(AB-BA)

                       Hence, we have  (AB-BA) = -(AB-BA)'

Thus,( AB-BA)' is skew symmetric.

Posted by

seema garhwal

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads