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Let $\mathrm{A}$ and $\mathrm{B}$ be any two $\mathrm{n} \times \mathrm{n}$ matrices such that the following conditions hold : $\mathrm{AB}=\mathrm{BA}$ and there exist positive integers $\mathrm{k}$ and $\ell$ such that $\mathrm{A}^{\mathrm{k}}=\mathrm{I}$ (the identity matrix) and $\mathrm{B}^{\prime}=0$ (the zero matrix). Then-
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The correct answer is:
$\operatorname{det}(\mathrm{AB})=0$
$A^{k}=I, B^{\ell}=0($ det $(B)=0)$
$\Rightarrow \operatorname{det}(A B)=0$
$\Rightarrow \operatorname{det}(A B)=0$
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