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Determinant Calculator — How It Works

Determinant Calculator math calculator arithmetic

Determinant Calculator — How It Works

The determinant of a 2×2 matrix is a single number that describes how the matrix scales area — and whether it flips orientation (negative determinant).

The formula

| a₁₁ a₁₂ |
| a₂₁ a₂₂ |  = (a₁₁ × a₂₂) − (a₁₂ × a₂₁)

Example

| 4 3 |
| 2 1 |  = (4×1) − (3×2) = 4 − 6 = -2

Why it matters

  • A determinant of 0 means the matrix is singular (not invertible) — its rows or columns are linearly dependent.
  • The sign tells you whether the transformation preserves or reverses orientation.
  • The magnitude is the area-scaling factor of the linear transformation.

Try the Determinant Calculator — instant results, no sign-up.

FAQ

Is this free?

Yes — the Determinant Calculator runs entirely in your browser, no sign-up required.