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Recall and Application Kronecker $$\delta$$ and Levi-Civita $$\epsilon$$ symbols

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1. Writing out all terms for a $$2\times 2$$ matrix $$A$$, explicitly verify that $\epsilon_{ij} \epsilon_{mn} A_{im} A_{jn} = 2\det A.$ where the indices $$i,j,m,n$$ take values 1 and 2.
2. For a three by three matrix A show that $\det A = \epsilon_{ijk} A_{i1}A_{j2} A_{k3}.$

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