A) A + B is symmetric
B) A - B is symmetric
C) AB + BA is symmetric
D) AB - BA is symmetric
Correct Answer: D
Solution :
Given, A and B are symmetric matrix of same order. \[\Rightarrow \] \[A=A',\,\,B=B'\] ?? (i) (i) \[(A+B)'=A'+B'=A+B\] [from Eq. (i)] \[\Rightarrow \] \[(A-B)\] is symmetric. (iii) \[(AB+BA)'=(AB)'+(BA)'\] \[=B'A'+A'B'\] \[=BA+AB\] [from Eq. (i)] \[=-(AB-BA)\] \[\Rightarrow \]\[(AB-BA)\] is skew - symmetric matrix.You need to login to perform this action.
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