Let $A, B, C$ be invertible $n × n$ matrices.
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$\det(B) = \frac {\det(ABC)}{\det(CA)}$
2026-04-25 19:26:40.1777145200
Determine if the statement below is (always) true. If true, justify your answer. If false, give a counterexample.
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Assuming $A,B,C \in GL_{n}(\mathbb{R})$,
$$\det(B) ~=~ \det(B)\bigg[\frac{\det(A)\cdot\det(C)}{\det(C)\cdot\det(A)}\bigg] ~=~ \frac{\det(ABC)}{\det(CA)}$$