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How does Mirror Image Interact with Invoke Duplicity?

A third level Trickery cleric gets mirror image as a domain spell. Invoke duplicity is a channel divinity ability gained at second level.

###Case 1 The cleric casts mirror image (which lasts for a minute) and then invokes duplicity, with which

you create a perfect illusion⁠ of yourself that lasts for 1 minute (PHB, Trickery Domain)

Does the perfect illusion bring with it the four mirror images? (We thought it did, but were not sure).

###Case 2 The cleric first invokes duplicity, and then casts mirror image through the duplicate since

you can cast Spells as though you were in the illusion’s space (PHB, Trickery Domain)

In this case, we thought that the cleric would not have the mirror images surrounding her, but that the duplicate would.

###Case 3
The cleric invokes duplicity, and then casts mirror image on herself. Does the duplicate have the mirror image magical effect on it?

We were trying to set it up such that both the cleric and the cleric's perfect duplicate had the mirror image magical effect surrounding her.

Three illusory duplicates of yourself appear in your space. Until the spell ends, the duplicates move with you and mimic your actions, shifting position so it’s impossible to track which image is real. (SRD, p. 165)

How does the interaction of mirror image and invoke duplicity work?

I was somewhat surprised to not find a Q&A already addressing this.