Given a matrix $A=\begin{pmatrix}a&b\\c&d\end{pmatrix}$, its transpose, obviously, is $A^T=\begin{pmatrix}a&c\\b&d\end{pmatrix}$. But is there a conventional way of notating the matrix $\begin{pmatrix}d&b\\c&a\end{pmatrix}$ in terms of $A$? This generalizes in an obvious way to larger matrices. Also, do you know of some instance where this has been useful, especially in a geometric application?

I realize this seems like a dumb question, but I'm working on something where this matrix operation has come up in a significant way. It would be nice to see if anyone has had something similar happen.

For now I've been using $^TA$.

Given a matrix $A=\begin{pmatrix}a&b\\c&d\end{pmatrix}$, its transpose, obviously, is $A^T=\begin{pmatrix}a&c\\b&d\end{pmatrix}$. But is there a conventional way of notating the matrix $\begin{pmatrix}d&b\\c&a\end{pmatrix}$ in terms of $A$? This generalizes in an obvious way to larger matrices. Also, do you know of some instance where this has been useful, especially in a geometric application?

I realize this seems like a dumb question, but I'm working on something where this matrix operation has come up in a significant way. It would be nice to see if anyone has had something similar happen.

For now I've been using $A_T$.