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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