Assume, a computer system has 4 users: Kate, Alice, Bob, and Mike. Kate owns file Katefile, the other three people can only read the file. Mike and Kate can read and write file Alicefile (owner Alice). Bob can only read and write the file Bobfile which he owns. Mike owns the file Mikefile and Bob and Kate can read and write the file Mikefile. Assume owner of files can execute it.

1. Create an access control matrix describing this system.
2. Suppose the owner of a file can add and remove permissions to that file. Mike removes Kate's permission and give permission to Alice to read and write Mikefile. Show the new access control matrix.
3. Suppose the commands to add or remove permissions can be written into a file, then that file is executed with the permissions of its owner. Does this change what operations are considered trusted? Explain.