Final answer:
A Log analysis tool would show output indicating systems administrators are logging into other users' inboxes via webmail by analyzing event and access logs. (option A)
Step-by-step explanation:
The tool that would show the type of output where systems administrators with privileged access are logging into other users' inboxes via webmail is a Log analysis tool. This type of tool is designed to analyze various types of logs where evidence of such activities would be recorded.
A log analysis tool is used to analyze and interpret log files that record user activities and system events. In this case, the log analysis tool would show a record of the administrators' login activities and identify when they accessed other users' inboxes. For example, log analysis tools can track and parse through event logs that show user authentication events, access logs from email servers, and any other system logs that record user activities. It would not be a password cracker, as these are used to decrypt passwords; neither would it be a command-line tool or a file integrity monitoring tool, which are used for direct system interaction and monitoring changes to files, respectively.