Q. 795.0( 1 Vote )

Fill in the blank

Answer :

B’AB is a symmetric matrix.

Proof:


Given A is symmetric matrix


A’=A ..(1)


Now in B’AB,


Let AB=C ..(2)


B’AB=B’C


Now Using Property (AB)’=B’A’


(B’C)’=C’(B’)’ (As (B’)’=B)


C’(B’)’=C’B


C’B=(AB)’B (Using Property (AB)’=B’A’)


(AB)’B=B’A’B (Using (1))


B’A’B= B’AB


Hence (B’AB)’= B’AB


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