@Rainmaker1973 My proof for clockwise rotation:
4 digit square number = 1000*(A) + 100*(A+3) + 10*(A+4) + (A+1),
where A is the starting digit
A + 3 is directly above A
A + 4 is up and right of A
A + 1 is right of A
= 1111*A + 341
= 11*(101*A + 31)
therefore always an integer multiple of 11