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<tex>\det (\mathcal{A} \cdot \mathcal{B}) {e_1} \land {e_2} \land... \land{e_n} = </tex><br><tex>
(\mathcal{A} \cdot \mathcal{B})^{\wedge_n}{e_1} \land {e_2} \land... \land{e_n} = ^{(*)}</tex><br><tex>
(\mathcal{A} \cdot \mathcal{B}) {e_1} \land (\mathcal{A} \cdot \mathcal{B}) {e_2} \land ... \land (\mathcal{A} \cdot \mathcal{B}) {e_n} = ^{(def(\mathcal{A} \cdot \mathcal{B}))}</tex><br><tex>
\mathcal{A} (\mathcal{B} {e_1}) \land \mathcal{A} (\mathcal{B} {e_2}) \land ... \land \mathcal{A} (\mathcal{B} {e_n}) = ^{(**)}</tex><br><tex>
\mathcal{A}^{\wedge_n}(\mathcal{B} {e_1} \land \mathcal{B} {e_2} \land ... \land \mathcal{B} {e_n})= ^{(***)}</tex><br><tex>
