Q. 805.0( 1 Vote )

Fill in the blanks in each of the

If A and B are symmetric matrices of same order, then AB is symmetric if and only if ______.

Answer :

This is only possible if A and B commute.

Proof:


Given A and B are symmetric matrices,


A’=A ..(1)


B’=B ..(2)


Let AB is a Symmetric matrix:-


(AB)’=AB


Using Property (AB)’=B’A’


B’A’=AB


Now using (1) and (2)


BA=AB


Hence A and B matrix commute.


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