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Determinant calculator

Calculate the determinant of a 3×3 matrix and see whether the matrix is invertible.

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Determinant calculator

Enter your values below and press Calculate to see your result instantly.

Matrix System [A] (3x3)
The Determinant |A|
-18
SPATIAL IMPACT
Volume Scaling
SYSTEM PROPERTY
Invertible
This matrix scales the volume of the space by a factor of |-18|.

About the Determinant calculator

Calculate the determinant of a 3×3 matrix and see whether the matrix is invertible.

How to use the Determinant calculator

  1. Fill in the nine entries of Matrix System [A].
  2. Press Calculate Scalar.

Formula and method

For a 2×2 matrix, det = ad − bc. For 3×3 matrices, expand along a row or use the rule of Sarrus. A non-zero determinant means the matrix has an inverse.

Worked example

The determinant of [[1, 2], [3, 4]] is 1×4 − 2×3 = −2.

Tips

  • A determinant of zero means the rows are linearly dependent and the matrix is singular.
  • Swapping two rows changes the sign of the determinant.

Frequently asked questions

What does the determinant tell me?
It shows how the matrix scales area or volume, and whether the matrix can be inverted.