Enter the four matrix elements.
Algebra Calculator
2×2 Matrix Calculator
Calculate determinant, trace, inverse, eigenvalues, and basic classification for a 2×2 matrix.
Instant answer
Formula breakdown
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Use the example values or replace them with your own. Required validation happens before the calculation.
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Calculated answer
Result
Simple workflow
How to use the 2×2 Matrix Calculator
Follow these steps to get a reliable result and understand how it was produced.
Calculate determinant ad−bc and trace a+d.
When determinant is non-zero, calculate the inverse and eigenvalues.
Understanding the calculation
A non-zero determinant means the matrix is invertible. The trace and determinant also determine the two eigenvalues.
det(A)=ad−bc; A⁻¹=(1/det)[[d,−b],[−c,a]]The result panel substitutes your numbers into this relationship and shows the important intermediate values.
Common uses
- Linear algebra homework
- Two-variable transformations
- Checking matrix invertibility
Accuracy tips
- A zero determinant means no inverse exists.
- Complex eigenvalues can occur.
- Decimal entries are supported.
Helpful answers
2×2 Matrix Calculator FAQs
Important details about formulas, inputs, limitations, and result interpretation.
What does determinant zero mean?
The matrix is singular and does not have an inverse.
What is the trace?
The trace is the sum of the main diagonal entries a+d.
Can eigenvalues be complex?
Yes, when the characteristic discriminant is negative.
Does this multiply matrices?
This tool focuses on properties of one 2×2 matrix.