Matrix Determinant Calculator (2×2) Formula

Understand the math behind the matrix determinant calculator (2×2). Each variable explained with a worked example.

Use the Matrix Determinant Calculator (2×2)

Formulas Used

Det

det = a * d - b * c

Trace

trace = a + d

Invertible

invertible = (a * d - b * c) != 0 ? 1 : 0

Variables

VariableDescriptionDefault
aa (row 1, col 1)3
bb (row 1, col 2)7
cc (row 2, col 1)1
dd (row 2, col 2)4

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 (-)

    • Worked Example

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

    a = 3b = 7c = 1d = 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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