Determinante 3×3
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
About this calculator
The 3×3 Determinant Calculator uses Sarrus' rule to calculate the determinant of a 3x3 square matrix. This rule is a practical and efficient method for calculating determinants of 3×3 matrices. It involves repeating the first two columns of the matrix to the right of the third column and then performing operations with the elements of the diagonals.
The Sarrus' rule formula for a 3×3 matrix is: det(A) = a(ei − fh) − b(di − fg) + c(dh − eg), where the matrix elements are represented by lowercase letters. This calculation is performed automatically by our calculator, providing the determinant of the entered matrix.
The 3×3 Determinant Calculator is useful in various areas, such as Linear Algebra, Numerical Calculus, and Physics. It can be used to solve systems of linear equations, find the inverse of a matrix, and determine the orientation of a set of vectors in three-dimensional space.
When using the calculator, it is essential to ensure that the entered matrix is a 3×3 matrix and that the elements are real numbers. Additionally, it is crucial to understand the concept of determinant and its application in specific problems to correctly interpret the results provided by the calculator.
Frequently asked questions
How does Sarrus' rule work?
Sarrus' rule is a method for calculating the determinant of a 3×3 matrix. It involves repeating the first two columns of the matrix to the right of the third column and performing operations with the elements of the diagonals.
What are the applications of the determinant of a 3×3 matrix?
The determinant of a 3×3 matrix has applications in various areas, such as Linear Algebra, Numerical Calculus, and Physics. It can be used to solve systems of linear equations, find the inverse of a matrix, and determine the orientation of a set of vectors.
What precautions should I take when using the calculator?
When using the calculator, it is essential to ensure that the entered matrix is a 3×3 matrix and that the elements are real numbers. Additionally, it is crucial to understand the concept of determinant and its application in specific problems.
Can the calculator be used for larger matrices?
No, this calculator is specific to 3×3 matrices. For larger matrices, it is necessary to use other methods or specific calculators.
How to interpret the result of the determinant?
The result of the determinant can be interpreted according to the context of the problem. A non-zero determinant indicates that the matrix is invertible and that the system of linear equations has a unique solution.