Calculate the determinant of a 2×2 matrix with complex numbers using our free Determinant Calculator. Get instant, accurate results with step-by-step solutions!
| Step | Description |
|---|---|
| 1 | Input matrix is [[1+i, 2], [3, 4-i]]. |
| 2 | For a 2×2 matrix [[a, b], [c, d]], the determinant is det = a*d – b*c. |
| 3 | Compute a*d = (1+i)*(4-i) = 4 – i + 4i – i² = 4 + 3i + 1 = 5 + 3i. |
| 4 | Compute b*c = 2*3 = 6. |
| 5 | Compute det = (5+3i) – 6 = -1 + 3i. |
| Final | Determinant: -1 + 3i. |
Determinant Calculator – Instantly Find the Determinant of Any Matrix
Need to calculate the determinant of a matrix quickly and correctly? Our Determinant Calculator makes it simple—no formulas, no errors, no headaches. Perfect for students, engineers, data scientists, and math enthusiasts!
What Is a Determinant Calculator?
The Determinant Calculator is an online tool that calculates the det(A) for any square matrix (2×2, 3×3, 4×4, etc.). The determinant is a single number that provides valuable insights about a matrix—like whether it’s invertible or singular, and how it scales space.
This calculator instantly finds the determinant and clearly tells you whether the matrix is non-singular (invertible) or singular (non-invertible).
How To Use the Determinant Calculator
- 👉 Choose the matrix size (2×2, 3×3, 4×4, etc.)
- 🔢 Enter the values in the matrix cells
- ✅ Click “Calculate”
- 📊 Get the exact determinant value instantly
No need to memorize cofactor expansion or perform Gaussian elimination by hand—the tool handles it all.
Why Use Our Tool?
| Feature | Benefit |
|---|---|
| 🧮 Supports All Matrix Sizes | Calculate determinants for 2×2 to larger square matrices |
| ⚡ Instant & Accurate | Get results in real time with zero error |
| 🧠 Educational Value | Great for learning linear algebra & matrix theory |
| 🆓 Completely Free | No sign-up, no fees, no ads |
| 📱 Mobile-Responsive | Use it easily on any device—phone, tablet, or desktop |
Who Should Use It?
- 🎓 Students working on algebra, calculus, or competitive exams
- 🧑🏫 Teachers explaining determinant concepts to classes
- 🧠 Engineers & Data Scientists solving systems of equations
- 👨💻 Programmers working with transformations, simulations, or graphics
- 🧮 Math Lovers exploring matrix properties and linear systems
FAQs
What does th
It indicates whether a matrix is invertible. If the determinant = 0, it’s singular and has no inverse.
What does the determinant tell us?
It indicates whether a matrix is invertible. If the determinant = 0, it’s singular and has no inverse.
Can this handle decimals or negative values?
Yes, you can input any real numbers—fractions, decimals, and negatives are fully supported.
What if I make a mistake in input?
You can easily correct any value or reset the entire matrix with one click.
Is this tool really free?
Absolutely! You can use it as many times as you want—completely free and unlimited.