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Question

If A and B are symmetric matrices then (AB + BA) is a matrix and (AB - BA) is a matrix.

A
skew - symmetric
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B
symmetric
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C
null
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D
identity
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Solution

The correct option is B symmetric
A and B are symmetricmatricesAT=A, BT=BNow,(AB+BA)T=BTAT+ATBT= (B)(A)+(A)(B)=BA+AB(AB+BA) is symm.(ABBA)T=BTATATBT= (B)(A)(A)(B)=BAAB=(ABBA)(ABBA) is skewsymm.

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