Let $A,B,$ and $D$ be invertible matrices of the same size, and assume that $D$ is diagonal. Which

of the following matrices is not symmetric in general?

$($A$)AD{A}^T$

$($B$)A+D+A^T$

$($C$)A^{-1}B{B}^T(A^T{)}^{-1}$

$($D$)A^{-1}BD{B}^{-1}(A^T{)}^{-1}$

$($E$)$ None