In mathematics, the determinant is a scalar value that is a function of the entries of a square matrix. It allows characterizing some properties of the matrix and the linear map represented by the matrix. In particular, the determinant is nonzero if and only if the matrix is invertible and the linear map represented by the matrix is an isomorphism. The determinant of a product of matrices is the product of their determinants (the preceding property is a corollary of this one).The determinant of a matrix A is denoted det(A), det A, or |A|.
In the case of a 2 × 2 matrix the determinant can be defined as
| A | = | a b c d | = a d − b c . {\displaystyle {\begin{aligned}|A|={\begin{vmatrix}a&b\\c&d\end{vmatrix}}=ad-bc.\end{aligned}}}Similarly, for a 3 × 3 matrix A, its determinant is
| A | = | a b c d e f g referenceEver curious about what that abbreviation stands for? fullforms has got them all listed out for you to explore. Simply,Choose a subject/topic and get started on a self-paced learning journey in a world of fullforms.
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