The numbers ai, bi, ci ( i =1,2,3 ) are called the elements of the determinant.

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

Determinants - Basic Concepts

where A1, B1 and C1 are the cofactors of a1, b1 and c1 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:

Determinants - Basic Concepts

These results are true for determinants of any order.

Determinants - Basic Concepts

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