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If $\mathrm{B}$ is a non-singular matrix and $\mathrm{A}$ is a square matrix, then the value of det $\left(\mathrm{B}^{-1} \mathrm{AB}\right)$ is equal to
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$\operatorname{det}(\mathrm{A})$
$\begin{aligned} &\left|\mathrm{B}^{-1} \mathrm{AB}\right|=\left|\mathrm{B}^{-1}\right||\mathrm{A}||\mathrm{B}| \\ &=\frac{1}{|\not{B} \mid}|\mathrm{A}||\not{B}| \quad \because \quad\left|\mathrm{B}^{-1}\right|=\frac{1}{|\mathrm{~B}|} \\ &=|\mathrm{A}| \end{aligned}$
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