Matrix Inverse Calculator (2×2)
Invert a 2×2 matrix and solve the linear system.
Enter your values
ⓘ Live results
Results
- Inverse row 1
- [0.6, -0.7]
- Inverse row 2
- [-0.2, 0.4]
- Determinant
- 10
- Solution x
- -0.4
- Solution y
- 2.8
Quick answer
The inverse of [[a, b], [c, d]] is 1/(ad − bc) × [[d, −b], [−c, a]], which exists only when the determinant ad − bc is non-zero.
A⁻¹ = 1/det × [[d, −b], [−c, a]]
How to use the Matrix Inverse Calculator (2×2)
- 1Enter the four matrix entries reading left to right, top to bottom.
- 2Read the inverse matrix.
- 3Optionally enter the right-hand side of your system to get x and y directly.
Worked example
Using the values the calculator loads with:
Inputs
- a (row 1, col 1)4
- b (row 1, col 2)7
- c (row 2, col 1)2
- d (row 2, col 2)6
- Right-hand side 1 (optional)18
- Right-hand side 2 (optional)16
Results
- Inverse row 1[0.6, -0.7]
- Inverse row 2[-0.2, 0.4]
- Determinant10
- Solution x-0.4
- Solution y2.8
Frequently asked questions
Why must the determinant be non-zero?
Dividing by the determinant is the last step of the formula; a zero determinant means the matrix collapses two dimensions into one and cannot be undone.
Can I check the answer?
Multiply the original by the inverse — you should get the identity matrix [[1,0],[0,1]].
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.