If A and B are symmetric matrices, which of the following matrices is symmetric? a) A^2-B^2 b) (A+B)(A-B) c) AB*AB

Stephanie Hunter 2022-07-26 Answered
If A and B are symmetric matrices, which of the following matrices is symmetric?
a) A 2 B 2
b) ( A + B ) ( A B )
c) A B A B
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Answers (1)

Caylee Davenport
Answered 2022-07-27 Author has 14 answers
Given that A and B are symmetric matrices.
That is A T = A , B T = B
Consider,
[ ( A + B ) ( A B ) ] T = ( A B ) T ( A + B ) T = ( A T B T ) ( A T + B T ) = ( A B ) ( A + B )
Not symmetric
Consider
A B A B [ A B A B ] T = A T B T A T B T = A B A B
which is symmetric.
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