Given a matrix $A_{\,3 \times 3}$, it is possible that there exist 8 functions or linear transformations such that they modify the matrix in the following way:
\begin{align} A = \begin{pmatrix} x & y & a_{13} \\ z & w & a_{23} \\ a_{31} & a_{32} & a_{33} \end{pmatrix} \qquad ; \qquad & T_{A-} \, (A) \ = \ \begin{pmatrix} z & x & a_{13} \\ w & y & a_{23} \\ a_{31} & a_{32} & a_{33} \end{pmatrix} \end{align}
Where $T_A$ rotates the elemets $a_{11}, \ a_{12},\ a_{21},\ a_{22}$, $\ $ $T_B$ rotates $a_{12}, \ a_{13}, \ a_{22}, \ a_{23}$, and so on. Also, the "-" rotates thoose elements clockwise, and the "+" sign, counterclockwise.
This can also be visualised here.
So, I wanted to ask, how would these transformations look like? I'm new to linear algebra and I tried to implement them with matrix multiplications but I didn't succeed that's why I wanted to ask for help on this problem.
The idea for this question came to me when I saw the problem of the Number Rotation Puzzle, I wanted to see if there is a way to represent the problem in linear algebra.
And that's about it, I will be attentive to any recommendations or comments.
Thank you so much for the help! Have a nice day.