2×2 determinant formula
For A = [[a,b],[c,d]], det(A) = ad − bc. For the sample [[1,2],[3,4]], the determinant is 1×4 − 2×3 = −2.
Calculators / Quick tool
Matrix Determinant Calculator
Calculate a two-by-two or three-by-three determinant from numeric rows.
● Processed locally in your browser
How to useHow to use Matrix Determinant Calculator ⌄
Calculate a two-by-two or three-by-three determinant from numeric rows.
- 1
Paste content, enter parameters or choose the files you need in “Comma-separated matrix rows”.
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Choose “2×2 determinant”, “3×3 determinant” for the job. Processing runs in this browser.
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Review the result under “Determinant”, then copy or download it after checking the output.
Result guide
What Matrix Determinant Calculator calculates
Choose the matrix size, enter one comma-separated row per line, and calculate det(A). The output shows the 2×2 diagonal formula or the 3×3 first-row cofactor expansion with your values substituted.
3×3 cofactor expansion
For the first row a, b, c, use a(ei−fh) − b(di−fg) + c(dh−eg). The result panel preserves this grouping so signs and each 2×2 minor can be checked directly.
What a zero determinant means
A zero determinant means the square matrix is singular: it has no unique inverse, its rows or columns are linearly dependent, and a related linear system may not have a unique solution.
Frequently asked questions
What input format should I use?
Enter one matrix row per line and separate entries with commas. A 3×3 matrix therefore needs exactly three lines with three numeric values on each line.
Does this calculator support larger matrices?
No. This page intentionally supports only 2×2 and 3×3 numeric matrices so it can show a compact, verifiable substitution. It does not claim support for symbolic or larger matrices.
Can a determinant be negative?
Yes. A determinant is a signed scalar. Its sign can reflect orientation, while its absolute value describes area or volume scaling for the linear transformation.
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