Let A be any square matrix of order 3 and $B =\begin{bmatrix}0&-4&2\\4&0&3\\-2&-3&0\end{bmatrix}$. Then the matrix $ABA^T$ is a

Skew symmetric matrix

The correct answer is Option (2) → Skew symmetric matrix

$B=\begin{pmatrix}0&-4&2\\4&0&3\\-2&-3&0\end{pmatrix}$

$B$ satisfies $B^{T}=-B$, therefore $B$ is a skew–symmetric matrix.

Consider the matrix $ABA^{T}$.

$(ABA^{T})^{T}=A\,B^{T}\,A^{T}=A(-B)A^{T}=-(ABA^{T})$

This shows that $ABA^{T}$ is also skew–symmetric.

The matrix $ABA^{T}$ is a skew–symmetric matrix.