if A and B are symmetric matrices, then ABA is

a-symmetric

b-skew-symmetric

c-diagonal

d-scalar

it is symmetric matrix  as (ABA)' = (A)'(AB)' = AB'A =ABA

hence it is symmetric matrix.

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a-symmetric matrix

A=A'  and  B=B'

(ABA)'=(BA)' (A)'=A'B' A'=ABA

now since (ABA)'=ABA;  hence ABA is a symmetric matrix

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Symmetric
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