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From Schaum's Outline in Tensor Calculus

If $A = [a_{ij}]_{nn} $ is any square matrix, then define $\text{ det } A = \epsilon_{i_1i_2i_3...i_{n-1}i_n}a_{1 \, \cdot \, i_1}a_{2 \, \cdot \, i_2}...a_{(n - 1) \, \cdot \, i_{n - 1}}a_{n \, \cdot \, i_n} $.

I can check this by expanding the product and sum in full, but what's the derivation or motivation behind this formula? I tried to find something on the Internet about this.

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