Is $\det(A^{-1}A)$ the same as $\det(A^{-1})\det(A)$

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Is the equation of $\det(A^{-1}A)$ the same as saying $\det(A^{-1})\det(A)$ ?

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$\det(AB) = \det(A) \cdot \det(B)$ for any square $A$ and $B$ of equal sizes.