The determinant is a mathematical property of a square matrix (matrix with equal number of columns and rows) that provides valuable information about the matrix. The determinant is denoted as det(A) or |A|, where A represents the matrix. The determinant is a single value that can be positive, negative, or zero.

The determinant carries several important properties and interpretations:

• Invertibility: A square matrix A is invertible (non-singular) if and only if its determinant is nonzero;
• Area or Volume Scaling: For 2x2 and 3x3 matrices, the determinant provides information about the scaling factor or the change in area/volume under a linear transformation represented by the matrix;
• Linear Independence: The determinant can determine whether a set of vectors is linearly independent. If the determinant of a matrix composed of vectors is nonzero, the vectors are linearly independent;
• Solution Existence: In systems of linear equations represented by matrices, the determinant can determine whether a unique solution exists. If the determinant is nonzero, a unique solution exists; otherwise, there may be no solution or an infinite number of solutions.

In Python, we can calculate determinant using np.linalg.det() method: