How to use the 2×2 matrix determinant and inverse calculator
Compute determinant, trace and inverse of a 2×2 matrix. Enter a₁₁, a₁₂, a₂₁, a₂₂ in the fields above; the determinant, trace, inverse a₁₁, inverse a₁₂, inverse a₂₁, inverse a₂₂ are computed instantly and plotted on the chart so you can see how the answer changes.
Formula
Variables
- a — a₁₁
- b — a₁₂
- c — a₂₁
- d — a₂₂
Worked example
With a₁₁ = 4, a₁₂ = 7, a₂₁ = 2, a₂₂ = 6, the calculator gives determinant ≈ 10; trace ≈ 10; inverse a₁₁ ≈ 0.6; inverse a₁₂ ≈ -0.7; inverse a₂₁ ≈ -0.2; inverse a₂₂ ≈ 0.4.
Frequently asked questions
What is the formula for the 2×2 matrix determinant and inverse calculation?
Determinant = a × d-b × c. Trace = a+d. Inverse a₁₁ = d / [Determinant]. Inverse a₁₂ = -b / [Determinant]. Inverse a₂₁ = -c / [Determinant]. Inverse a₂₂ = a / [Determinant]. Here a is a₁₁, b is a₁₂, c is a₂₁, d is a₂₂.
What inputs do I need for the 2×2 matrix determinant and inverse calculator?
You need a₁₁, a₁₂, a₂₁, a₂₂. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use this calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.