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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 ______.
If A and B are symmetric matrices of same order, then AB is symmetric if and only if ______.
Answers (1)
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.
View full answer
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