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If A and B are symmetric matrices of the...

If A and B are symmetric matrices of the same order then (A) A-B is skew symmetric (B) A+B is symmetric (C) AB-BA is skew symmetric (D) AB+BA is symmetric

A

skew symmetric matrix

B

symmetric symmetric matrix

C

zero matrix

D

identity matrix

Text Solution

Verified by Experts

The correct Answer is:
A
A and B are symmetric matrices ,
`therefore A'=A and B'=B`
No (AB-BA)'=(AB)' (BA)'
`=B'A'-A'b'=B'A-Ab=-(AB-BA)`
`implies ` (AB-BA) is a skew symmetric matrix
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