A determinant is a special number that can be calculated from a square matrix in mathematics. It provides important information about the matrix, such as whether it is invertible or singular. If the determinant is zero, the matrix does not have an inverse, meaning it cannot be used to solve certain equations. In geometry, the determinant can also represent the area or volume of shapes defined by vectors. For example, the determinant of a 2x2 matrix can give the area of a parallelogram formed by two vectors, while a 3x3 matrix can represent the volume of a parallelepiped.