To give a concrete example, matrix multiplication is not commutative in general (AB ≠ BA), but e.g. multiplication with the identity matrix is (AI = IA). So AIB = ABI ≠ BAI.

Or applied to the programming example, the statements:

    1. Server.accept
    2. Client.connect
    3. File.write  # write to completely unrelated file

123 = 312 ≠ 321.