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Determinant calculator
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
- Fill in the nine entries of Matrix System [A].
- 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
It shows how the matrix scales area or volume, and whether the matrix can be inverted.