3x3 Matrix Determinant Calculator
Determinant of a 3x3 matrix by cofactor expansion.
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ⓘ Live results
Results
- Determinant
- -3
- Singular?
- No — matrix is invertible
Quick answer
The determinant is found by expanding along the first row with alternating signs and 2x2 sub-determinants.
det = a(ei-fh) - b(di-fg) + c(dh-eg)
How to use the 3x3 Matrix Determinant Calculator
- 1Enter the nine entries of the matrix row by row.
- 2Cofactor expansion along the first row is applied automatically.
- 3A determinant of zero means the matrix has no inverse.
Worked example
Using the values the calculator loads with:
Inputs
- a1
- b2
- c3
- d4
- e5
- f6
- g7
- h8
- i10
Results
- Determinant-3
- Singular?No — matrix is invertible
Frequently asked questions
What does a zero determinant mean?
The matrix is singular — its rows/columns are linearly dependent.
Can I use this for a 2x2 matrix?
Use the dedicated matrix determinant calculator for 2x2 matrices instead.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.