Answer
$A=BCB^{-1}$
Work Step by Step
$AB=BC\qquad $ ... Right-multiply with $B^{-1}:$
$ABB^{-1}=BCB^{-1}$
$A(BB^{-1})=BCB^{-1}$
$AI=BCB^{-1}$
$A=BCB^{-1}$
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