To the best of my knowledge, the Allegory of the Cave is just a literary device that is used in Plato's
The Republic, and is not an independent work (so no italics) or a named part of such a work (so no quotation marks). Thus:
The Exploration of the Meaning of Reality in the Allegory of the Cave and
The Matrix
This assumes that your title refers specifically to how these works explore the meaning of reality, rather than identifying your own work as an exploration of how these works present the meaning of reality (in which case, use "An Exploration").
Quotation marks are incorrect for
The Matrix because it is an independent work. Underline is incorrect if typed, but an adequate substitute for italics if written by hand.
As a general point for the report, it is my best guess that Allegory of the Cave should be capitalized (like I just did) when it appears in normal prose, but not italicized/bolded/written in your own blood/etc. Wikipedia, where people are usually insanely anal about such things, is
inconsistent about the capitalization.