1.11.8 Tensor calculus

Problem: Let \( a=\operatorname{det}\left(a_{i k}\right) \) for tensor \( a_{i k} \). Prove that \[ a=\frac{1}{6} \varepsilon_{i j k} \cdot \varepsilon^{m n p} \cdot a_{i m} \cdot a_{j n} \cdot a_{k p}, \] where \( \varepsilon_{i j k} \) is Levi - Civita symbol.