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If $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are three vectors such that $|\mathbf{a}|=1,|\mathbf{b}|=2,|\mathbf{c}|=3$ and $2 \mathbf{a} \cdot \mathbf{b}=\mathbf{b} \cdot \mathbf{c}=\mathbf{c} \cdot \mathbf{a}=2$, Then, $[\mathbf{a} \mathbf{b} \mathbf{c}]^2=$
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15
$[\mathbf{a} \mathbf{b} \mathbf{c}]^2=\left|\begin{array}{lll}\mathbf{a} \cdot \mathbf{b} & \mathbf{a} \cdot \mathbf{b} & \mathbf{a} \cdot \mathbf{c} \\ \mathbf{b} \cdot \mathbf{a} & \mathbf{b} \cdot \mathbf{b} & \mathbf{b} \cdot \mathbf{c} \\ \mathbf{c} \cdot \mathbf{a} & \mathbf{c} \cdot \mathbf{b} & \mathbf{c} \cdot \mathbf{c}\end{array}\right|=\left|\begin{array}{lll}1 & 1 & 2 \\ 1 & 4 & 2 \\ 2 & 2 & 9\end{array}\right|=15$
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