A) skewsymmetric
B) Symmetric
C) neither symmetric nor skewsymmetric
D) I or - I, where I is an identity matrix.
Correct Answer: B
Solution :
Let A be symmetric matrix and B be skew symmetric matrix. \[\therefore \]\[{{A}^{T}}=A\]and \[{{B}^{T}}=-B\] Consider \[{{(AB-BA)}^{T}}={{(AB)}^{T}}-{{(BA)}^{T}}\] \[={{B}^{T}}{{A}^{T}}-{{A}^{T}}{{B}^{T}}\] \[=(-B)(A)-(A)(-B)\] \[=-BA+AB=AB-BA\] This shows AB - BA is symmetric matrix.
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