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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