Question

# Prove that the matrix $$B'AB$$ is symmetric or skew symmetric according as $$A$$ is symmetric or skew symmetric.

Solution

## If $$A$$ be symmetric i.e., $$A'=A$$ then$$(B'AB)'=[B'(AB)]'=(AB)'(B')'$$$$=(B'A')B=B'A'B=B'AB$$Hence $$B'AB$$ is symmetricIf $$A$$ is skew symmetric i.e., $$A'=-A$$ then$$(B'AB)'=[B'(AB)]'=(AB)'(B')'$$$$=(B'A')B=B'(-A)B=-(B'AB)$$$$\therefore$$ $$B'AB$$ is skew symmetricMathematics

Suggest Corrections

0

Similar questions
View More

People also searched for
View More