1. Chapter 3 Class 12 Matrices
  2. Serial order wise
  3. Miscellaneous

Misc. 4 - Chapter 3 Class 12 Matrices

Last updated at May 29, 2018 by

Misc 4 - If A and B are symmetric matrices, prove AB - BA is - Miscellaneous

  1. Chapter 3 Class 12 Matrices
  2. Serial order wise

    3. Miscellaneous

    Formation and order of matrix →

Transcript

Misc. 4 If A and B are symmetric matrices, prove that AB − BA is a skew symmetric matrix. Given A and B are symmetric matrices ∴ A’ = A and B’ = B Now, (AB – BA)’ = (AB)’ – (BA)’ = B’A’ – A’B’ = BA – AB = − (AB – BA) ∴ (AB – BA)’ = − (AB – BA) Thus, (AB − BA) is a skew-symmetric matrix. Hence proved

Chapter 3 Class 12 Matrices
Serial order wise

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.