no prism-like triangle for colour correction in my fcp

Whenever FCP behaves strangely for no apparent reason you should delete the preferences as it can often rectify the problem.

Hold down the command and option keys as you launch FCP until the delete preferences/settings window appears.

What shows up in the Inspector depends on what is selected.

Do you have a clip selected in the timeline? If you do and still do not see the prism then do what Ian said. If you have a clip selected in the browser, not the timeline, then it’s normal.

Which version?