Determinants

A determinant is a number associated with a square matrix (a grid of numbers with equal rows and columns) that reveals certain properties of the matrix. It helps determine whether the matrix has an inverse (i.e., can be "undone" or reversed) and provides information about the volume scaling factor when transforming space through that matrix. For example, if the determinant is zero, the matrix compresses space into a lower dimension, making it singular and not invertible. Determinants are useful in solving systems of equations, understanding geometric transformations, and in various areas of mathematics and engineering.