Determinante 2×2
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
det = ad − bc
About this calculator
The 2×2 determinant calculator computes the determinant of a 2×2 square matrix using the formula det = ad − bc. Simply enter the values of a, b, c, and d, and the result is displayed instantly. It is a useful tool for students of linear algebra, engineering, and areas involving linear systems.
The calculation is straightforward: for a matrix [[a, b], [c, d]], multiply a by d and subtract the product of b by c. The determinant indicates whether the matrix is invertible (nonzero value) or singular (zero). This is essential for solving systems of equations, computing eigenvalues, and in linear transformations.
Use this calculator when you need to quickly check if a 2×2 matrix has an inverse, or in geometry exercises (area of a parallelogram) and physics problems involving determinants. It is ideal for verifying manual results or speeding up repetitive calculations.
Caution: the order of elements in the matrix matters. The determinant changes sign if rows or columns are swapped. Also, ensure the matrix is truly 2×2; for larger matrices, use a specific calculator. Decimal or fractional values are accepted, but avoid typos.
Frequently asked questions
What does it mean if the determinant is zero?
It means the matrix has no inverse (is singular) and its rows or columns are linearly dependent.
Can I use decimal numbers or fractions?
Yes, the calculator accepts decimals and fractions. Just enter the values correctly.
How is the determinant related to the area of a parallelogram?
The absolute value of the determinant of a 2×2 matrix formed by the vectors of a parallelogram gives its area.
What if I enter the values in the wrong order?
The result will be different. Follow the standard order: a (row1, col1), b (row1, col2), c (row2, col1), d (row2, col2).
Does this calculator work for 3×3 matrices?
No, it is exclusively for 2×2 matrices. For larger matrices, use an appropriate determinant calculator.