Find the determinant, inverse, transpose or trace of a matrix.
Calculated instantly in your browser.
How do you calculate the determinant, inverse, transpose or trace of a matrix?
The determinant is computed by cofactor expansion; the inverse by Gauss–Jordan elimination; the transpose swaps rows and columns; the trace sums the diagonal. The determinant, inverse and trace need a square matrix; a determinant of zero means it is singular with no inverse. For [[1, 2], [3, 4]] the determinant is −2 and the inverse is [[−2, 1], [1.5, −0.5]].
Understanding your result
The determinant, inverse and trace require a square matrix; the transpose works for any shape. A determinant of zero means the matrix is singular and has no inverse.
Formula and method
The determinant is computed by cofactor expansion; the inverse by Gauss–Jordan elimination; the transpose swaps rows and columns; the trace sums the diagonal.
Assumptions and limitations
The determinant, inverse and trace need a square matrix, while the transpose accepts any shape. A determinant of zero means the matrix is singular and has no inverse. Results are floating-point approximations, so near-singular or ill-conditioned matrices can lose precision, and very large matrices may be slow or numerically unstable.
Worked example
For [[1, 2], [3, 4]] the determinant is −2 and the inverse is [[−2, 1], [1.5, −0.5]].
How to use this tool
- Enter your matrix, one row per line.
- Choose determinant, inverse, transpose or trace.
- Read the result.
Common mistakes to avoid
- Entering rows of different lengths.
- Asking for the inverse of a singular matrix.
About the Matrix Calculator
The Matrix Calculator computes the determinant, inverse, transpose or trace of a matrix. Enter your matrix with one row per line and choose an operation.
Who should use this tool
Students and engineers working with linear algebra.
Benefits
- Determinant, inverse, transpose and trace.
- Handles any size for transpose; square for the rest.
- Detects singular (non-invertible) matrices.
- Clean grid output.
Practical use cases
- Checking a determinant or inverse by hand.
- Solving a linear-algebra exercise.
- Transposing data for a calculation.
Frequently asked questions
Why is there no inverse?
A matrix has no inverse when its determinant is zero — it is singular. The calculator detects this and tells you.
What sizes are supported?
Any rectangular matrix for the transpose, and square matrices for the determinant, inverse and trace.
Why does the inverse show messy decimals like 0.333333?
The inverse is computed with floating-point arithmetic, so exact fractions such as one third become repeating decimals that are rounded for display. The values are correct to within tiny rounding error. If you need exact fractions, take the displayed determinant and adjugate and simplify the ratios by hand.