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 AandBaresymmetricmatrices⇒AT=A,BT=BNow,(AB+BA)T=BTAT+ATBT=(B)(A)+(A)(B)=BA+AB⇒(AB+BA)issymm.(AB−BA)T=BTAT−ATBT=(B)(A)−(A)(B)=BA−AB=−(AB−BA)⇒(AB−BA)isskew−symm.