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Suppose $A$, $B$, and $C$ are all invertible matrices of the same shape.

Which of the following matrices is the inverse of $AB^2C^2$?

$C^2B^2A$

$A^{-1}B^{-2}C^{-2}$

$C^{-2}B^{-2}A^{-1}$

$AB^2C^2$