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Calculation Machine

Determinant Calculator

2×2 and 3×3 matrix determinants.

Reviewed by the Calculation Machine team · How we check our maths

Your values

ⓘ Live results

Results
Determinant
10
Invertible?
Yes
Matrix size
2×2
Area/volume scale factor
10

Quick answer

The determinant measures how a matrix scales area or volume; a determinant of zero means the matrix is singular.

The formula

det[[a,b],[c,d]] = ad − bc

Worked example

Worked example

Using the values the calculator loads with.

Inputs

  • Matrix size2×2
  • Matrix values row by row4, 7, 2, 6

Result

  • Determinant10
  • Invertible?Yes
  • Matrix size2×2
  • Area/volume scale factor10

How to use the Determinant Calculator

  1. 1Choose the matrix size.
  2. 2Enter values row by row, separated by commas.
  3. 3A zero determinant means no inverse exists.

Frequently asked questions

What does a negative determinant mean?

The transformation flips orientation as well as scaling.

Why does zero matter?

The matrix collapses space to a lower dimension, so it cannot be inverted.

About this calculator