Determinant

In mathematics, invariant of square matrices

In mathematics, the determinant is a scalar-valued function of the entries of a square matrix that has many properties which make it fundamental for the study of square matrices and linear transformations represented by them. The determinant of a matrix A is commonly denoted det(A), det A, or |A|. For square matrices of dimensions two and three, the determinant is explicitly described as det [ a b c d ] = a d − b c , det [ a b c d e f g h i ] = a e i + b f g + c d h − c e g − b d i − a f h .

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