Last updated: August 1, 2026
Matrix Determinant Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Quick Answer
Enter a square matrix in row format to compute its determinant. The calculator also reports the matrix size and whether the matrix is singular. A zero determinant means the matrix is not invertible, while a nonzero determinant confirms that an inverse exists.
Enter a square matrix to compute its determinant and to see immediately whether the matrix is singular.
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
For 2×2 matrices, det([[a,b],[c,d]]) = ad - bc. Larger cases are computed by elimination.
Where:
- A=square matrix
- det(A)=determinant of A
Worked Examples
2×2 determinant
Compute det([[1,2],[3,4]]).
- 1Use ad - bc.
- 2Calculate 1×4 - 2×3.
Identity matrix
The identity determinant is 1.
- 1Use the diagonal product.
- 2Read 1 directly.
Singular matrix
One row is a multiple of another.
- 1Reduction creates a zero row.
- 2The determinant becomes zero.
Decimal matrix
Use 2.5,1;4,3.
- 1Apply elimination or the 2×2 formula.
- 2Round the final answer if needed.
Introduction
Compute the determinant of a square matrix and immediately see whether the matrix is singular.
Overview
Compute the determinant of a square matrix and immediately see whether the matrix is singular.
Determinant
Invertibility checks
Area and volume scaling
Cramer-style system solving
Input format
Enter a square matrix in row form, such as 1,2;3,4.
Separate rows with semicolons
Separate entries with commas or spaces
Brackets are optional
Keep row lengths consistent
Formula and method
For 2×2 matrices, det([[a,b],[c,d]]) = ad - bc. Larger cases are computed by elimination.
- A matters:
square matrix.
- Det(A) matters:
determinant of A.
Validation rules
The calculator uses deterministic validation before it computes the final result.
The matrix must be nonempty and square
Every entry must be finite
Malformed rows are rejected
Outputs are rounded to six decimals
Interpreting the outputs
Use the main result first, then the secondary fields to verify the structure and meaning of the answer.
A zero determinant means the matrix is singular
A nonzero determinant means the matrix is invertible
matrixSize confirms the accepted dimension
The determinant sign tracks orientation changes
Common use cases
These are typical reasons to use this calculator in study or applied work.
Invertibility checks
Area and volume scaling
Cramer-style system solving
Characteristic polynomial work
FAQs
Can I compute the determinant of a rectangular matrix?
No. Determinants are defined only for square matrices.
What does a zero determinant mean?
It means the matrix is singular and does not have an inverse.
Why does the sign matter?
The sign indicates whether the associated transformation preserves or reverses orientation.
Can I use decimals?
Yes. Any finite real entries are supported.
How do I enter a 3×3 matrix?
Use a format like 1,2,3;4,5,6;7,8,9.
Does the calculator use cofactor expansion?
No. It uses elimination, which is faster and more stable for larger examples.