Are these kind of matrices generally known in mathematics? Do they have a name?
$ \left[\begin{array}{rrr} A & B \\ B & A \\ \end{array}\right] $
$ \left[\begin{array}{rrr} A & B & C \\ C & A & B \\ B & C & A \\ \end{array}\right] $
$ \left[\begin{array}{rrr} A & B & C & D \\ D & A & B & C \\ C & D & A & B \\ B & C & D & A \\ \end{array}\right] $
$ \left[\begin{array}{rrr} A & B & C & D & E \\ E & A & B & C & D \\ D & E & A & B & C \\ C & D & E & A & B \\ B & C & D & E & A \\ \end{array}\right] $
The main thing is that each letter will be in the same columnn/row just once. I'm trying to do some combination calculations with big matrices following this pattern, so knowing effective ways to generate and compute these would help.
(The pattern here is that the next row is made by shifting the previous row to one right.)