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.
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.