The numbers a_{i}, b_{i}, c_{i} ( i =1,2,3 ) are called the **elements of the determinant**.

The determinant obtained by deleting the i^{th} row and j^{th} column is called the minor of the element at the i^{th} row and the j^{th} column. The cofactor of this element is (-1)^{i+j} (minor).

where A_{1}, B_{1} and C_{1} are the cofactors of a_{1}, b_{1} and c_{1} respectively. i.e., the sum of products of the elements of any row (column) of a determinant with the corresponding co-factors is equal to the value of the determinant.

We can expand the determinant through any row or column. It means that we can write:

These results are true for determinants of any order.

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