Matrix Algebra Tool
Determinant Calculator
Find det(A) for square matrices from 2×2 to 8×8. This calculator supports integers, decimals, and fractions like 1/2, -3/4, or 7/5, and returns both the exact fractional determinant and a decimal approximation.
Enter your matrix values
Choose the matrix size, then fill in each entry. You can type values such as 5, -2, 3/4, or 0.5. The calculator uses exact fraction arithmetic internally, which helps avoid rounding errors.
Method used:
The calculator computes the determinant using exact fraction-preserving Gaussian elimination. Row swaps change the sign of the determinant, and the determinant equals the product of the pivots after elimination.
The calculator computes the determinant using exact fraction-preserving Gaussian elimination. Row swaps change the sign of the determinant, and the determinant equals the product of the pivots after elimination.
Exact Determinant
0
Decimal Approximation
0.000000
Matrix Size
2 × 2
Matrix Type
General
Invertible?
No
det(A) exact fraction
0
det(A) decimal value
0.000000
Sign of determinant
Zero
Determinant status
Singular matrix
No calculation yet.
This calculator keeps fractions exact whenever possible. Even for larger matrices, the fraction result is mathematically exact, while the decimal result is shown for convenience.
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