About the 2×2 Matrix Calculator
All-in-one 2×2 matrix calculator: determinant, inverse, transpose, trace and rank of a two-by-two matrix.
Also known as: 2x2 matrix, 2 by 2 matrix, 2x2 determinant, 2x2 inverse.
How to use this calculator
- Enter 2×2 matrix.
- The result updates instantly as you type — press Calculate (or Enter) at any time.
- Review the breakdown shown under the main result.
- Use Copy result or Share to save the answer or send a link with your inputs.
Formula
det = ad − bc · A⁻¹ = (1/det)[d −b; −c a]
Worked example
Using the values pre-filled in the calculator above:
- 2×2 matrix: 4 7 2 6
the calculator returns:
- Determinant: 10
- Inverse: [ 0.6 -0.7 ] [ -0.2 0.4 ]
- Transpose: [ 4 2 ] [ 7 6 ]
- Trace: 10