Can I Modify Order to Get X=I Matrix?

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If I have ABCXC^-1A^-1B^-1=I (that is C, B, A inverse), can I modify the order so that the AA^-1, BB^-1 are multiplied to get the identity matrix so that I can get it down to X=I?
 
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It's a clue to change the equation so that it keeps the equality.
For example trying premultiplying the inverse of A...
 
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