Matrix Determinant Calculator

How it works

1. 1Choose the matrix size n ∈ {2, 3, 4} — the grid resizes automatically.
2. 2Enter each entry of square matrix A; cells default to 0.
3. 3The determinant is computed via Gaussian elimination with partial pivoting and displayed immediately.

Use cases

• Checking whether a system of linear equations has a unique solution (det ≠ 0) or is singular (det = 0).
• Verifying that a transformation matrix preserves volume before applying it in 3-D graphics or physics simulations.
• Computing the scaling factor of a linear map in multivariate calculus (change-of-variables formula).

Frequently asked questions

What does a determinant of zero mean?

A zero determinant means the matrix is singular — its rows (or columns) are linearly dependent, it has no inverse, and the corresponding system of equations either has no solution or infinitely many.

Why does the sign of the determinant matter?

A negative determinant means the linear transformation reverses orientation (like a reflection). Its absolute value still gives the volume-scaling factor, but the sign encodes handedness.

How accurate is the result for large matrices?

The calculator uses Gaussian elimination with partial pivoting, which is numerically stable for most inputs. For 4×4 matrices with entries spanning many orders of magnitude, small floating-point rounding may appear in the last decimal places.