determinant

A determinant is a special number associated with a square matrix (a grid of numbers). It provides useful information about the matrix, such as whether it has an inverse (meaning it can be "undone") or how it changes space when applied. Geometrically, for a 2x2 matrix, the absolute value of the determinant tells you the area of a parallelogram formed by the vectors represented by the matrix. For larger matrices, it relates to volume or higher-dimensional analogs. In essence, the determinant captures how the matrix transforms space—scaling, flipping, or collapsing it.