Q. 785.0( 1 Vote )

Fill in the blank

Answer :

(i) AB – BA is a Skew Symmetric matrix


Given A’=A and B’=B


(AB-BA)’=(AB)’-(BA)’


(AB)’-(BA)’=B’A’-A’B’


B’A’-A’B’=BA-AB=-(AB-BA)


(AB-BA)’=-(AB-BA) (skew symmetric matrix)


Eg. Let A =


B=


AB= and BA=


AB-BA=


(AB-BA)’=


-(AB-BA)=


(ii) BA – 2AB is a Neither Symmetric nor Skew Symmetric matrix


Given A’=A and B’=B


(BA-2AB)’=(BA)’-(2AB)’


(BA)’-(2AB)’=A’B’-2B’A’


A’B’-2B’A’=AB-2BA=-(2BA-AB)


(BA-2AB)’=-(2BA-AB)


Eg. Let A =


B=


AB= and BA=


BA-2AB=


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