Determinant
![The area of the parallelogram is the absolute value of the determinant of the matrix formed by the vectors representing the parallelogram's sides.](/Images/godic/202501/08/Area_parallellogram_as_determinant.svg3847.png")
![The volume of this parallelepiped is the absolute value of the determinant of the matrix formed by the rows constructed from the vectors r1, r2, and r3.](/Images/godic/202501/08/Determinant_parallelepiped.svg3847.png")
![Sarrus' rule: The determinant of the three columns on the left is the sum of the products along the solid diagonals minus the sum of the products along the dashed diagonals](/Images/godic/202501/08/Sarrus_rule.svg3847.png")
In linear algebra, the determinant is a useful value that can be computed from the elements of a square matrix. The determinant of a matrix A is denoted det(A), det A, or |A|.
In the case of a 2 × 2 matrix, the specific formula for the determinant is simply the upper left element times the lower right element, minus the product of the other two elements. Similarly, suppose we have a 3 × 3 matrix A, and we want the specific formula for its determinant |A|: