Matrix Determinant Calculator

Calculate the determinant and trace of an entered three-by-three matrix and identify singular cases.

Categories Calculators Topics Research & Fieldwork
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Evaluate a three-by-three determinant from visible entries

Enter the nine values of a three-by-three matrix in row order. The calculator expands the determinant, reports the trace and indicates whether the numeric result is effectively zero. Keeping every coefficient visible makes the tool useful for checking linear-algebra exercises, coordinate transforms and small systems without uploading a file or entering a specialized matrix syntax.

Interpret a near-zero result with numerical care

A zero determinant means the matrix is singular in exact arithmetic, but decimal inputs and floating-point calculations can produce a very small residual instead of exact zero. The tool uses a tolerance for its status label and does not calculate an inverse, eigenvalues or conditioning. Use numerical linear-algebra software when stability and error bounds matter.

Frequently asked questions

Which matrix size is supported?

This page accepts one three-by-three matrix.

What does a zero determinant mean?

In exact arithmetic it means the matrix is singular and has no inverse.

Why is a tolerance used?

Floating-point input can create tiny residuals around an exact zero.