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  4. If A and B are square matrices of the same order and if A=AT,B=BT, then (ABA)T=

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Q. If $A$ and $B$ are square matrices of the same order and if $A=A^{T},B=B^{T},$ then $\left(ABA\right)^{T}=$

KEAMKEAM 2015Matrices

Solution:

Let$ P =(A B A)^{T}=A^{T} B^{T} A^{T} $
$ A =A^{T}, B=B^{T}=A B A $