When to use this calculator
Find the inverse of a non-singular two-by-two matrix. Output uses a semicolon to separate rows. Nearly singular matrices are sensitive to rounding.
Explore the algebra & number calculators for other questions in this topic. For a related calculation, use the Two Equation Linear System Calculator: Solve two simultaneous linear equations in two unknowns.
PUTTING IT INTO PRACTICE
Two by Two Matrix Inverse: a worked example
The values below are an illustrative example, not a recommendation. Replace them with measurements or assumptions that match your question.
| Input | Example value |
|---|---|
| Top left | 1 |
| Top right | 2 |
| Bottom left | 3 |
| Bottom right | 4 |
| Result | -2, 1; 1.5, -0.5 |
- Check the input labels and enter the example values above.
- Apply the relationship: Inverse = 1/(ad−bc) × rows (d,−b) and (−c,a)..
- The result is -2, 1; 1.5, -0.5 , rounded for display.
How to interpret your result
Output uses a semicolon to separate rows. Nearly singular matrices are sensitive to rounding.
Identify whether the question asks for one term, a total or a count of possible selections. Sequences use a fixed difference or ratio. In counting problems, order and replacement determine the correct model.
Frequently asked questions
Do combinations and permutations count the same thing?
No. Combinations ignore the order of selection; permutations count different orders separately.
When is the two by two matrix inverse calculator useful?
Find the inverse of a non-singular two-by-two matrix. Output uses a semicolon to separate rows. Nearly singular matrices are sensitive to rounding.
How do I use the two by two matrix inverse calculator?
Enter top left, top right, bottom left, bottom right. The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Inverse = 1/(ad−bc) × rows (d,−b) and (−c,a)..
What should I check before using the result?
Output uses a semicolon to separate rows. Nearly singular matrices are sensitive to rounding.
How are results rounded?
Scalar numbers display up to six decimal places, with scientific notation for very large or small values. Text, fraction, date and schedule outputs use the format described on the tool. Intermediate calculations use JavaScript floating-point arithmetic. Keep sensible precision for your measurements.
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