The term determinant was first introduced by Gauss in 1801 while discussing quadratic forms. He used the term because the determinant determines the properties of the quadratic forms.

To every **square matrix** A of order n with entries as real or complex numbers, you can associate **a number called determinant** of matrix A and it is denoted by |A| or det(A) or ∆.

**Difference between a matrix and a determinant**

- A matrix cannot be reduced to a number. That means a matrix is a structure alone and is not having any value. But a determinant can be reduced to a number.
- The number of rows may not be equal to the number of columns in a matrix. In a determinant the number of rows is always equal to the number of columns.
- On interchanging the rows and columns, a different matrix is formed. In a determinant interchanging the rows and columns does not alter the value of the determinant.