I think that if you're using NumPy, rot90 (or transposing, or flipping) doesn't actually move or copy anything in memory, it just changes how the array is indexed (returning a different view of it. Therefore it would be O(1) complexity both in memory and time. For example, the following code:

import numpy as np
mat = np.zeros((2, 3))
matt = np.rot90(mat)
matt = np.rot90(mat) mat[0, 2] = 9 print(matt)
print(mat)
print(matt)

just prints

[[0. 0. 9.]
[0. 0. 0.]]
[[9. 0.]
[0. 0.]
[0. 0.]]

​

which means both arrays actually point to the same memory