u_{33}\\\end{bmatrix}}}  (upper triangular matrix).නිර්ණායකය[සංස්කරණය]ප්‍රධාන ලිපිය: DeterminantA linear transformation on R2 given by the indicated matrix. The determinant of this matrix is −1, as the area of the green parallelogram at the right is 1, but the map reverses the orientation, since it turns the counterclockwise orientation of the vectors to a clockwise one.The determinant det(A) or |A| of a square matrix A is a number encoding certain properties of the matrix. A matrix is invertible if and only if its determinant is nonzero. Its absolute value equals the area (in R2) or volume (in R3) of the image of the unit square (or cube), while its sign corresponds to the orientation of the corresponding linear map: the determinant is positive if and only if the orientation is preserved. The determinant of 2-by-2 matrices is given bydet(abcd)=ad−bc.{\displaystyle \det {\begin{pmatrix}a&b\\c&d\end{pmatrix}}=ad-bc.}When the determinant 