Determinant:

The value of a determinant is the sum of the products of elements of a row (or a column) with their corresponding cofactors.

• The value of the determinant remains unchanged if its rows and columns are interchanged.
• If two rows or columns of a determinant are interchanged then the determinant retains its absolute value but its sign is changed.
• If any two rows or columns of a determinant are identical then its value is zero.
• If each element of a row or a column of a determinant is multiplied by a constant k then the value of the new determinant is k times the value of the original determinant.

For a square matrix A of order n,

• If any two rows or columns of a determinant are proportional then its value is zero.
• If each element of a row 9or column) of a determinant is expressed as a sum of two or more terms then the determinant can be expressed as the sum of two or more determinants.
• If to any row or column of a determinant, a multiple of another row or column is added, the value of the determinant remains the same.