DefinitionThe determinant of a square matrix is a value associated with the matrix that represents some properties of that square matrix such as invertibility, volume scaling factor, or whether the linear vectors of the square matrix are linearly independent. The determinant of a square matrix A,det(A) can be computed using cofactor expansion, row reduction, or eigenvalue decomposition, for example. Determinants are widely used in linear algebra as the value that can be computed from a matrix to solve systems of linear equations, compute the inverse of a square matrix, or analyse transformations of geometrical transformations of vectors or matrices. The determinant of a 2x2 Matrix with entries [a b c d] is given by the value ad – bc, while the value of a 3x3 Matrix can be computed using the Sarrus rule or expansion by minors.
