Math
2×2 matrix determinant
Calculate the determinant of a two-by-two matrix.
Calculators / Math / 2×2 matrix inverse
2×2 matrix inverse calculator
Find the determinant and inverse of a nonsingular 2×2 matrix.
On this page
Determinant10
Inverse top left0.6
Inverse top right-0.7
Inverse bottom left-0.2
Inverse bottom right0.4
Calculator controls
How to calculate
Find the determinant and inverse of a nonsingular 2×2 matrix.
A⁻¹ = 1/(ad − bc) × [[d, −b], [−c, a]]
Worked example
Top left a: 4; Top right b: 7; Bottom left c: 2; Bottom right d: 6.
Determinant: 10 ; Inverse top left: 0.6 ; Inverse top right: -0.7 ; Inverse bottom left: -0.2 ; Inverse bottom right: 0.4 .
Assumptions and limits
Only square matrices with a nonzero determinant have an inverse. Numerical conditioning is not assessed.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Find the determinant and inverse of a nonsingular 2×2 matrix. Every assumption remains visible so the result can be checked or changed.
When this tool is useful
Use the 2×2 matrix inverse for an initial estimate, comparison, or classroom calculation.
Understanding your inputs
| Input | What to enter |
|---|---|
| Top left a | Enter a number of at least -1000000000000 and no more than 1000000000000. |
| Top right b | Enter a number of at least -1000000000000 and no more than 1000000000000. |
| Bottom left c | Enter a number of at least -1000000000000 and no more than 1000000000000. |
| Bottom right d | Enter a number of at least -1000000000000 and no more than 1000000000000. |
Frequently asked questions
What are the limits of this 2×2 matrix inverse?
Only square matrices with a nonzero determinant have an inverse. Numerical conditioning is not assessed.
Can I use different units?
Use the units printed beside each field. Convert measurements first when your source uses different units.