Matrix Determinant Calculator

Calculate the determinant of a 2×2 matrix. Also shows whether the matrix is invertible.

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Det

5.0000

Trace7.0000
Invertible1
View formula & how it works →

2×2 Matrix Determinant

Formula

For matrix [[a, b], [c, d]]:

det = ad - bc

Properties

  • If det = 0, the matrix is singular (not invertible)
  • If det ≠ 0, the matrix is invertible
  • det gives the area scaling factor of the linear transformation
  • sign of det indicates whether orientation is preserved (+) or reversed (-)

    • Example Calculation

    Find the determinant of [[3, 7], [1, 4]].

    1. 01det = (3)(4) - (7)(1)
    2. 02= 12 - 7
    3. 03= 5
    4. 04Since det ≠ 0, the matrix is invertible

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