 Hello friends welcome to the session. I am Alka. We are going to discuss matrices We have given that show that matrix B transpose AB is symmetric or skew symmetric according as a is symmetric or skew symmetric Now let's start with the solution our case case first is when a is Symmetric therefore When a is symmetric we can say a transpose equal to a now V transpose AB pole transpose equal to V transpose a transpose transpose of V transpose this is equal to V transpose a transpose and transpose of a transpose is a Matrix that is V. So we get V transpose a V pole transpose equal to V transpose a B that's V transpose AB is symmetric if a is Symmetric Now our case second is when a is skew symmetric. So this implies a Transpose equal to minus a this is our second equation now V transpose a V Whole transpose equal to V transpose a transpose V transpose transpose equal to V transpose minus a and B This is equal to minus V transpose a B hence transpose of V transpose AB equal to minus V transpose a B Hence we conclude that B transpose AB is skew symmetric if a is skew symmetric Hence we conclude that V transpose AB is symmetric or skew symmetric according as a is symmetric or skew symmetric Hope you understood the solution and enjoyed the session. Goodbye and take care